Publication

文章千古事，得失寸心知。—— 唐 · 杜甫

Research Papers

You can find my papers on Google Scholar or on arXiv

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  How Focused Are LLMs? A Quantitative Study via Repetitive Deterministic Prediction Tasks

  Wanda Hou , Leon Zhou , Hong-Ye Hu , Yi-Zhuang You , Xiao-Liang Qi

  ArXiv Preprint arXiv:2511.00763 (2025)

  We investigate the performance of large language models on repetitive deterministic prediction tasks and study how the sequence accuracy rate scales with output length. Each such task involves repeating the same operation n times. Examples include letter replacement in strings following a given rule, integer addition, and multiplication of string operators in many body quantum mechanics. If the model performs the task through a simple repetition algorithm, the success rate should decay exponentially with sequence length. In contrast, our experiments on leading large language models reveal a sharp double exponential drop beyond a characteristic length scale, forming an accuracy cliff that marks the transition from reliable to unstable generation. This indicates that the models fail to execute each operation independently. To explain this phenomenon, we propose a statistical physics inspired model that captures the competition between external conditioning from the prompt and internal interference among generated tokens. The model quantitatively reproduces the observed crossover and provides an interpretable link between attention induced interference and sequence level failure. Fitting the model to empirical results across multiple models and tasks yields effective parameters that characterize the intrinsic error rate and error accumulation factor for each model task pair, offering a principled framework for understanding the limits of deterministic accuracy in large language models.

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  Designing Shadow Tomography Protocols by Natural Language Processing

  Yadong Wu , Pengfei Zhang , Ce Wang , Juan Yao , Yi-Zhuang You

  ArXiv Preprint arXiv:2509.12782 (2025)

  Quantum circuits form a foundational framework in quantum science, enabling the description, analysis, and implementation of quantum computations. However, designing efficient circuits, typically constructed from single- and two-qubit gates, remains a major challenge for specific computational tasks. In this work, we introduce a novel artificial intelligence-driven protocol for quantum circuit design, benchmarked using shadow tomography for efficient quantum state readout. Inspired by techniques from natural language processing (NLP), our approach first selects a compact gate dictionary by optimizing the entangling power of two-qubit gates. We identify the iSWAP gate as a key element that significantly enhances sample efficiency, resulting in a minimal gate set of {I, SWAP, iSWAP}. Building on this, we implement a recurrent neural network trained via reinforcement learning to generate high-performing quantum circuits. The trained model demonstrates strong generalization ability, discovering efficient circuit architectures with low sample complexity beyond the training set. Our NLP-inspired framework offers broad potential for quantum computation, including extracting properties of logical qubits in quantum error correction.

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  Machine learning the effects of many quantum measurements

  Wanda Hou , Samuel J Garratt , Norhan M Eassa , Eliott Rosenberg , Pedram Roushan , Yi-Zhuang You , Ehud Altman

  ArXiv Preprint arXiv:2509.08890 (2025)

  Measurements are essential for the processing and protection of information in quantum computers. They can also induce long-range entanglement between unmeasured qubits. However, when post-measurement states depend on many non-deterministic measurement outcomes, there is a barrier to observing and using the entanglement induced by prior measurements. Here we demonstrate a new approach for detecting such measurement-induced entanglement. We create short-range entangled states of one- and two-dimensional arrays of qubits in a superconducting quantum processor, and aim to characterize the long-range entanglement induced between distant pairs of qubits when we measure all of the others. To do this we use unsupervised training of neural networks on observations to create computational models for post-measurement states and, by correlating these models with experimental data, we reveal measurement-induced entanglement. Our results additionally demonstrate a transition in the ability of a classical agent to accurately model the experimental data; this is closely related to a measurement-induced phase transition. We anticipate that our work can act as a basis for future experiments on quantum error correction and more general problems in quantum control.

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  Measurement-Based Quantum Diffusion Models

  Xinyu Liu , Jingze Zhuang , Wanda Hou , Yi-Zhuang You

  ArXiv Preprint arXiv:2508.08799 (2025)

  We introduce measurement-based quantum diffusion models that bridge classical and quantum diffusion theory through randomized weak measurements. The measurement-based approach naturally generates stochastic quantum trajectories while preserving purity at the trajectory level and inducing depolarization at the ensemble level. We address two quantum state generation problems: trajectory-level recovery of pure state ensembles and ensemble-average recovery of mixed states. For trajectory-level recovery, we establish that quantum score matching is mathematically equivalent to learning unitary generators for the reverse process. For ensemble-average recovery, we introduce local Petz recovery maps for states with finite correlation length and classical shadow reconstruction for general states, both with rigorous error bounds. Our framework establishes Petz recovery maps as quantum generalizations of reverse Fokker-Planck equations, providing a rigorous bridge between quantum recovery channels and classical stochastic reversals. This work enables new approaches to quantum state generation with potential applications in quantum information science.

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  Dual-unitary shadow tomography

  Ahmed A Akhtar , Namit Anand , Jeffrey Marshall , Yi-Zhuang You

  Quantum, 1816 (2025)

  We introduce “dual-unitary shadow tomography''(DUST), a classical shadow tomography protocol based on dual-unitary brick-wall circuits. To quantify the performance of DUST, we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left-or right-movers. We develop a mean-field description of the Pauli weight in terms of , which represents the probability of having nontrivial support at site and depth starting from a fixed weight distribution. We develop an equation of state for and simulate it numerically using Monte Carlo simulations. For the task of predicting operators with (nearly) full support, we show that DUST outperforms brick-wall Clifford shadows of equal depth. This advantage is further pronounced for small system sizes and our results are generally robust to finite-size effects.

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  Sequential learning on a Tensor Network Born machine with Trainable Token Embedding

  Wanda Hou , Miao Li , Yi-Zhuang You

  Machine Learning: Science and Technology (2025)

  Generative models aim to learn the probability distributions underlying data, enabling the generation of new, realistic samples. Quantum-inspired generative models, such as Born machines based on the matrix product state (MPS) framework, have demonstrated remarkable capabilities in unsupervised learning tasks. This study advances the Born machine paradigm by introducing trainable token embeddings through positive operator-valued measurements (POVMs), replacing the traditional approach of static tensor indices. Key technical innovations include encoding tokens as quantum measurement operators with trainable parameters and leveraging QR decomposition to adjust the physical dimensions of the MPS. This approach maximizes the utilization of operator space and enhances the model's expressiveness. Empirical results on RNA data demonstrate that the proposed method significantly reduces …

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  Strange correlator and string order parameter for non-invertible symmetry protected topological phases in 1+ 1d

  Da-Chuan Lu , Fu Xu , Yi-Zhuang You

  ArXiv Preprint arXiv:2505.00673 (2025)

  In this paper, we construct strange correlators and string order parameters for non-invertible symmetry protected topological phases (NISPTs) in 1+1d quantum lattice spin models. The strange correlator exhibits long-range order when evaluated between two distinct NISPTs and decays exponentially otherwise. We show that strange charged operators inserted into the strange correlator are linked to the interface algebra (boundary tube algebra) and are non-trivial when all its irreducible representations have dimensions greater than one. We discuss the generalization to higher dimensions. The string order parameter is obtained by contracting the truncated symmetry operator with charge decoration operators, which are determined by the NISPT action tensors. We illustrate the above construction using the three NISPTs of and demonstrate the extraction of categorical data via tensor networks, particularly through the ZX calculus. Finally, we show that the entanglement spectrum degeneracy is determined by the irreducible representations of the interface algebra when assuming non-invertible symmetry on-site condition.

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  Monte Carlo Simulation of Operator Dynamics and Entanglement in Dual-Unitary Circuits

  Menghan Song , Zhaoyi Zeng , Ting-Tung Wang , Yi-Zhuang You , Zi Yang Meng , Pengfei Zhang

  Quantum, 1681 (2025)

  We investigate operator dynamics and entanglement growth in dual-unitary circuits, a class of locally scrambled quantum systems that enables efficient simulation beyond the exponential complexity of the Hilbert space. By mapping the operator evolution to a classical Markov process, we perform Monte Carlo simulations to access the time evolution of local operator density and entanglement with polynomial computational cost. Our results reveal that the operator density converges exponentially to a steady-state value, with analytical bounds that match our simulations. Additionally, we observe a volume-law scaling of operator entanglement across different subregions, and identify a critical transition from maximal to sub-maximal entanglement growth, governed by the circuit’s gate parameter. This transition, confirmed by both mean-field theory and Monte Carlo simulations, provides new insights into operator entanglement dynamics in quantum many-body systems. Our work offers a scalable computational framework for studying long-time operator evolution and entanglement, paving the way for deeper exploration of quantum information dynamics.

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  Demonstration of robust and efficient quantum property learning with shallow shadows

  Hong-Ye Hu , Andi Gu , Swarnadeep Majumder , Hang Ren , Yipei Zhang , Derek S Wang , Yi-Zhuang You , Zlatko Minev , Susanne F Yelin , Alireza Seif

  Nature Communications (1), 2943 (2025)

  Extracting information efficiently from quantum systems is crucial for quantum information processing. Classical shadows enable predicting many properties of arbitrary quantum states using few measurements. While random single-qubit measurements are experimentally friendly and suitable for learning low-weight Pauli observables, they perform poorly for nonlocal observables. Introducing a shallow random quantum circuit before measurements improves sample efficiency for high-weight Pauli observables and low-rank properties. However, in practice, these circuits can be noisy and bias the measurement results. Here, we propose the robust shallow shadows, which employs Bayesian inference to learn and mitigate noise in postprocessing. We analyze noise effects on sample complexity and the optimal circuit depth. We provide theoretical guarantees for the success of error mitigation under a wide class of …

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  Deconfined criticality as intrinsically gapless topological state in one dimension

  Sheng Yang , Fu Xu , Da-Chuan Lu , Yi-Zhuang You , Hai-Qing Lin , Xue-Jia Yu

  ArXiv Preprint arXiv:2503.01198 (2025)

  Deconfined criticality and gapless topological states have recently attracted growing attention, as both phenomena go beyond the traditional Landau paradigm. However, the deep connection between these two critical states, particularly in lattice realization, remains insufficiently explored. In this Letter, we reveal that certain deconfined criticality can be regarded as an intrinsically gapless topological state without gapped counterparts in a one dimensional lattice model. Using a combination of field-theoretic arguments and large-scale numerical simulations, we establish the global phase diagram of the model, which features deconfined critical lines separating two distinct spontaneous symmetry breaking ordered phases. More importantly, we unambiguously demonstrate that the mixed anomaly inherent to deconfined criticality enforces topologically robust edge modes near the boundary, providing a general mechanism by which deconfined criticality manifests as a gapless topological state. Our findings not only offer a new perspective on deconfined criticality but also deepen our understanding of gapless topological phases of matter.

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  Holographic classical shadow tomography

  Shuhan Zhang , Xiaozhou Feng , Matteo Ippoliti , Yi-Zhuang You

  Physical Review B (5), 054306 (2025)

  We introduce “holographic shadows,” a new class of randomized measurement schemes for classical shadow tomography that achieves the optimal scaling of sample complexity for learning geometrically local Pauli operators at any lengthscale, without the need for fine-tuning protocol parameters such as circuit depth or measurement rate. Our approach utilizes hierarchical quantum circuits, such as tree quantum circuits or holographic random tensor networks. Measurements within the holographic bulk correspond to measurements at different scales on the boundary (i.e., the physical system of interests), facilitating efficient quantum state estimation across observable at all scales. Considering the task of estimating stringlike Pauli observables supported on contiguous intervals of sites in a one-dimensional system, our method achieves an optimal sample complexity scaling of , with the local Hilbert …

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  Machine Learning for Ground State Preparation via Measurement and Feedback

  Chuanxin Wang , Yi-Zhuang You

  ArXiv Preprint arXiv:2502.06517 (2025)

  We present a recurrent neural network-based approach for ground state preparation utilizing mid-circuit measurement and feedback. Unlike previous methods that use machine learning solely as an optimizer, our approach dynamically adjusts quantum circuits based on real-time measurement outcomes and learns distinct preparation protocols for different Hamiltonians. Notably, our machine learning algorithm consistently identifies a state preparation strategy wherein all initial states are first steered toward an intermediate state before transitioning to the target ground state. We demonstrate that performance systematically improves as a larger fraction of ancilla qubits are utilized for measurement and feedback, highlighting the efficacy of mid-circuit measurements in state preparation tasks.

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  Data driven modeling for self-similar dynamics

  Ruyi Tao , Ningning Tao , Yi-zhuang You , Jiang Zhang

  Physica D: Nonlinear Phenomena, 134505 (2025)

  Multiscale modeling of complex systems is crucial for understanding their intricacies. In recent years, data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. Still, at present,this field is more focused on the prediction or control problems in specific fields, and there is no suitable framework to help us promote the establishment of complex system modeling theory. On the other hand, self-similarity is prevalent in complex systems, hinting that large-scale complex systems can be modeled at a reduced cost. In this paper, we introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge, facilitating the modeling of self-similar dynamical systems. Our framework can discern whether the dynamics are self-similar to deterministic dynamics. For uncertain dynamics, it not only can judge whether it is self-similar or not, but …

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  Symmetry protected topological phases under decoherence

  Jong Yeon Lee , Yi-Zhuang You , Cenke Xu

  Quantum, 1607 (2025)

  We investigate mixed states exhibiting nontrivial topological features, focusing on symmetry-protected topological (SPT) phases under various types of decoherence. Our findings demonstrate that these systems can retain topological information from the SPT ground state despite decoherence. In the''doubled Hilbert space,''we define symmetry-protected topological ensembles (SPT ensembles) and examine boundary anomalies in this space. We generalize the concept of the strange correlator, initially used to diagnose SPT ground states, to identify anomalies in mixed-state density matrices. Through exact calculations of stabilizer Hamiltonians and field theory evaluations, we show that nontrivial features of SPT states persist in two types of strange correlators: type-I and type-II. The type-I strange correlator reveals SPT information that can be efficiently detected and used experimentally, such as in preparing long-range entangled states. The type-II strange correlator encodes the full topological response of the decohered mixed state, reflecting the SPT state's pre-decoherence presence. Our work offers a unified framework for understanding decohered SPT phases from an information-theoretic perspective.

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  Renormalization group flow, optimal transport, and diffusion-based generative model

  Artan Sheshmani , Yi-Zhuang You , Baturalp Buyukates , Amir Ziashahabi , Salman Avestimehr

  Physical Review E (1), 015304 (2025)

  Diffusion-based generative models represent a forefront direction in generative artificial intelligence (AI) research today. Recent studies in physics have suggested that the renormalization group (RG) can be conceptualized as a diffusion process. This insight motivates us to develop a diffusion-based generative model by reversing the momentum-space RG flow. We establish a framework that interprets RG flow as optimal transport gradient flow, which minimizes a functional analogous to the Kullback-Leibler divergence, thereby bridging statistical physics and information theory. Our model applies forward and reverse diffusion processes in Fourier space, exploiting the sparse representation of natural images in this domain to efficiently separate signal from noise and manage image features across scales. By introducing a scale-dependent noise schedule informed by a dispersion relation, the model optimizes …

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  Topological Responses of the Standard Model Gauge Group

  Zheyan Wan , Juven Wang , Yi-Zhuang You

  ArXiv Preprint arXiv:2412.21196 (2024)

  The local Lie algebra of the Standard Model (SM) is , yet its global gauge group, SU(3) SU(2) U(1)/ , q remains undetermined. Building on previous work on 4d anomalies and 5d cobordism invariants, we classify lower-dimensional invertible field theories (iFTs) or symmetry-protected topological states (SPTs) in 4d, 3d, 2d, and 1d. While the integer SPTs are hard to detect, the fractional SPTs produce measurable topological responses. In particular, the symmetry fractionalization labeled by in [arXiv:2411.18160] introduces the symmetry-enriched SM variants, denoted as SM . We further introduce a new integer series of baryon-minus-lepton -like U(1) symmetries, with electroweak hypercharge , , , where the charge . Analyzing the symmetry-enriched SM with 0-form and 1-form symmetries , symmetry-twist group homomorphism , and symmetry frationalization obstruction , their spacetime-internal gauge bundle constraints, and their mixed anomalies, we derive the fractional topological response Our response requires more general Spin manifolds for odd and Spin manifolds for even . For a given (with and ), uniquely fixes the gauge group parameter q and fractionalization label . Moreover, using pairs such as , etc. uniquely distinguishes SM . Our results illuminate the global structure of the SM gauge group via measurable topological responses.

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  Quantum Many-Body Lattice CRT Symmetry: Fractionalization, Anomaly, and Symmetric Mass Generation

  Yang-Yang Li , Juven Wang , Yi-Zhuang You

  ArXiv Preprint arXiv:2412.19691 (2024)

  Charge conjugation (C), mirror reflection (R), and time reversal (T) symmetries, along with internal symmetries, are essential for massless Majorana and Dirac fermions. These symmetries are sufficient to rule out potential fermion bilinear mass terms, thereby establishing a gapless free fermion fixed point phase, pivotal for symmetric mass generation (SMG) transition. In this work, we systematically study the anomaly of C-R-T-internal symmetry in all spacetime dimensions by analyzing the projective representation (i.e. the fractionalization) of the C-R-T-internal symmetry group in the quantum many-body Hilbert space on the lattice. By discovering the fermion-flavor-number-dependent C-R-T-internal symmetry's anomaly structure, we demonstrate an alternative way to derive the minimal flavor number for SMG, which shows consistency with known results from K\"ahler-Dirac fermion or cobordism classification. Our findings reveal that, in general spatial dimensions, either 8 copies of staggered Majorana fermions or 4 copies of staggered Dirac fermions admit SMG. By directly searching for 4-fermion interactions that form commuting stabilizers respecting all symmetry constraints, we can prove the explicit SMG gapping retained a unique ground state in the codespace. Furthermore, we establish the correspondence between the symmetry operators of staggered fermions and free fermions, which is instrumental in facilitating the analysis of symmetry fractionalization at the field theory level.

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  Machine Learning Symmetry Discovery for Classical Mechanics

  Wanda Hou , Molan Li , Yi-Zhuang You

  ArXiv Preprint arXiv:2412.14632 (2024)

  In this study, we propose a data-driven, deep-learning-based Machine-Learning Symmetry Discovery (MLSD) algorithm to automate the discovery of continuous Lie group symmetries in classical mechanical systems from their time-evolution trajectory data. MLSD uses neural networks (NNs) to predict conserved physical quantities that implement symmetry transformations of the phase space coordinates. After training, MLSD is able to identify the Lie algebra, particularly non-abelian ones, as indicated by the Lie algebra structure coefficients. To demonstrate the effectiveness of the MLSD method, we applied it to simulated data from the classical three-dimensional Kepler problem and the harmonic oscillator. The results show that the algorithm successfully identified the hidden symmetry groups of both systems.

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  CRT Fractionalization in the First Quantized Hamiltonian Theory

  Yang-Yang Li , Zheyan Wan , Juven Wang , Shing-Tung Yau , Yi-Zhuang You

  ArXiv Preprint arXiv:2412.11958 (2024)

  Recent research has revealed that the CRT symmetry for fermions exhibits a fractionalization distinct from the for scalar bosons. In fact, the CRT symmetry for fermions can be extended by internal symmetries such as fermion parity, thereby forming a group extension of the direct product. Conventionally, a Majorana fermion is defined by one Dirac fermion with trivial charge conjugation. However, when the spacetime dimension , the real dimension of Majorana fermion (dim ) aligns with the real dimension of Dirac fermion (dim ), rather than being half, which necessitates the introduction of a symplectic Majorana fermion, defined by two Dirac fermions with trivial charge conjugation. To include these two types of Majorana fermions, we embed the theory in and define the Majorana fermion field as a representation of the real Clifford algebra with 8-fold periodicity. Within the Hamiltonian formalism, we identify the 8-fold CRT-internal symmetry groups across general dimensions. Similarly, Dirac fermion field is defined as a representation of the complex Clifford algebra with 2-fold periodicity. Interestingly, we discover that the CRT-internal symmetry groups exhibit an 8-fold periodicity that is distinct from that of the complex Clifford algebra. In certain dimensions where distinct mass terms can span a mass manifold, the CRT-internal symmetries can act non-trivially upon this mass manifold. Employing domain wall reduction method, we are able to elucidate the relationships between symmetries across different dimensions.

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  Contractive unitary and classical shadow tomography

  Yadong Wu , Ce Wang , Juan Yao , Hui Zhai , Yi-Zhuang You , Pengfei Zhang

  ArXiv Preprint arXiv:2412.01850 (2024)

  The rapid development of quantum technology demands efficient characterization of complex quantum many-body states. However, full quantum state tomography requires an exponential number of measurements in system size, preventing its practical use in large-scale quantum devices. A major recent breakthrough in this direction, called classical shadow tomography, significantly reduces the sample complexity, the number of samples needed to estimate properties of a state, by implementing random Clifford rotations before measurements. Despite many recent efforts, reducing the sample complexity below for extracting any non-successive local operators with a size remains a challenge. In this work, we achieve a significantly smaller sample complexity of using a protocol that hybridizes locally random and globally deterministic unitary operations. The key insight is the discovery of a deterministic global unitary, termed as \textit{contractive unitary}, which is more efficient in reducing the operator size to enhance tomography efficiency. The contractive unitary perfectly matches the advantages of the atom array quantum computation platform and is readily realized in the atom array quantum processor. More importantly, it highlights a new strategy in classical shadow tomography, demonstrating that a random-deterministic hybridized protocol can be more efficient than fully random measurements.

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  Realizing triality and p-ality by lattice twisted gauging in (1+1)d quantum spin systems

  Da-Chuan Lu , Zhengdi Sun , Yi-Zhuang You

  SciPost Physics (5), 136 (2024)

  In this paper, we study the twisted gauging on the (1+ 1) d lattice and construct various non-local mappings on the lattice operators. To be specific, we define the twisted Gauss law operator and implement the twisted gauging of the finite group on the lattice motivated by the orbifolding procedure in the conformal field theory, which involves the data of non-trivial element in the second cohomology group of the gauge group. We show the twisted gauging is equivalent to the two-step procedure of first applying the SPT entangler and then untwisted gauging. We use the twisted gauging to construct the triality (order 3) and -ality (order ) mapping on the symmetric Hamiltonians, where is a prime. Such novel non-local mappings generalize Kramers-Wannier duality and they preserve the locality of symmetric operators but map charged operators to non-local ones. We further construct quantum process to realize these non-local mappings and analyze the induced mappings on the phase diagrams. For theories that are invariant under these non-local mappings, they admit the corresponding non-invertible symmetries. The non-invertible symmetry will constrain the theory at the multicritical point between the gapped phases. We further give the condition when the non-invertible symmetry can have symmetric gapped phase with a unique ground state.

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  ShadowGPT: Learning to Solve Quantum Many-Body Problems from Randomized Measurements

  Jian Yao , Yi-Zhuang You

  ArXiv Preprint arXiv:2411.03285 (2024)

  We propose ShadowGPT, a novel approach for solving quantum many-body problems by learning from randomized measurement data collected from quantum experiments. The model is a generative pretrained transformer (GPT) trained on simulated classical shadow data of ground states of quantum Hamiltonians, obtained through randomized Pauli measurements. Once trained, the model can predict a range of ground state properties across the Hamiltonian parameter space. We demonstrate its effectiveness on the transverse-field Ising model and the cluster-Ising model, accurately predicting ground state energy, correlation functions, and entanglement entropy. This approach highlights the potential of combining quantum data with classical machine learning to address complex quantum many-body challenges.

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  Strong Pairing Originated from an Emergent Z2 Berry Phase in La3Ni2O7

  Jia-Xin Zhang , Hao-Kai Zhang , Yi-Zhuang You , Zheng-Yu Weng

  Physical Review Letters (12), 126501 (2024)

  The recent discovery of high-temperature superconductivity in offers a fresh platform for exploring unconventional pairing mechanisms. Starting with the basic argument that the electrons in orbitals nearly form local moments, we examine the effect of the Hubbard interaction on the binding strength of Cooper pairs based on a single-orbital bilayer model with intralayer hopping and interlayer superexchange . By extensive density matrix renormalization group calculations, we observe a remarkable enhancement in binding energy as much as 10–20 times larger with increasing from 0 to 12 at . We demonstrate that such a substantial enhancement stems from a kinetic-energy-driven mechanism. Specifically, a Berry phase will emerge at large due to the Hilbert space restriction (Mottness), which strongly suppresses the mobility of single particle propagation as compared to …

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  Frequency Domain Diffusion Model with Scale-Dependent Noise Schedule

  Amir Ziashahabi , Baturalp Buyukates , Artan Sheshmani , Yi-Zhuang You , Salman Avestimehr

  2024 IEEE International Symposium on Information Theory (ISIT), 19-24 (2024)

  Diffusion models have played a crucial role in the recent advancements in generative image modeling. These models are characterized by a forward process that incrementally corrupts images. The modeling objective is to develop a reverse process capable of reconstructing the original image from degraded inputs so that the trained model can then be leveraged to generate natural images from pure noise. In this work, we introduce a novel diffusion process that operates in the frequency domain. Typically, the frequency domain representation of an image exhibits a sparse structure, with energy predominantly concentrated in low frequency components. This inherent sparsity aids us in the effective separation of signal and noise during the reverse process. We utilize this property to introduce a scale-dependent noise schedule, offering precise control over various image scales. Working in the frequency domain …

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  Optical conductivity in symmetric mass generation insulators

  Meng Zeng , Fu Xu , Da-Chuan Lu , Yi-Zhuang You

  ArXiv Preprint arXiv:2405.05339 (2024)

  Symmetric mass generation (SMG) insulators are interaction-driven, featureless Mott insulating states in quantum many-body fermionic systems. Recent advancements suggest that zeros in the fermion Green's function could lead to non-vanishing negative optical conductivity in SMG insulators, even below the charge excitation gap. This study explores the origin of this unusual behavior through the lens of pole-zero duality, highlighting a critical issue where the current operator becomes unbounded, rendering the response function unphysical. By employing a lattice model, we derive a well-behaved lattice regularization of the current operator, enabling a detailed study of optical conductivity in SMG insulators. Utilizing both analytical and numerical methods, including strong-coupling expansions, we confirm that SMG insulators exhibit no optical conductivity at low energies below the charge gap, effectively resolving the paradox. This work not only deepens our understanding of quantum many-body phenomena but also lays a robust theoretical groundwork for future experimental explorations of SMG materials.

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  Disorder operator and Rényi entanglement entropy of symmetric mass generation

  Zi Hong Liu , Yuan Da Liao , Gaopei Pan , Menghan Song , Jiarui Zhao , Weilun Jiang , Chao-Ming Jian , Yi-Zhuang You , Fakher F Assaad , Zi Yang Meng , Cenke Xu

  Physical Review Letters (15), 156503 (2024)

  The “symmetric mass generation” (SMG) quantum phase transition discovered in recent years has attracted great interest from both condensed matter and high energy theory communities. Here, interacting Dirac fermions acquire a gap without condensing any fermion bilinear mass term or any concomitant spontaneous symmetry breaking. It is hence beyond the conventional Gross-Neveu-Yukawa-Higgs paradigm. One important question we address in this Letter is whether the SMG transition corresponds to a true unitary conformal field theory. We employ the sharp diagnosis including the scaling of disorder operator and Rényi entanglement entropy in large-scale lattice model quantum Monte Carlo simulations. Our results strongly suggest that the SMG transition is indeed an unconventional quantum phase transition and it should correspond to a true unitary conformal field theory.

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  Dual-unitary classical shadow tomography

  Ahmed A Akhtar , Namit Anand , Jeffrey Marshall , Yi-Zhuang You

  ArXiv E-prints arXiv:2404.01068 (FERMILAB-PUB-24-0504-SQMS-V; arXiv: 2404) (2024)

  We introduce a classical shadow tomography scheme based on dual-unitary brick-wall circuits termed "dual-unitary shadow tomography" (DUST). For this we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a final measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. We first show that dual-unitaries must have a minimal amount of entropy production. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of , which represents the probability of having nontrivial support at site and depth starting from a fixed weight distribution. We develop an equation of state for , and simulate it numerically using Monte Carlo simulations. Lastly, we demonstrate that the fast-thermalizing properties of dual-unitary circuits make them better at predicting large operators than shallow brick-wall Clifford circuits. Our results are robust to finite-size effects due to the chirality of dual-unitary brick-wall circuits.

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  Observing schrödinger’s cat with artificial intelligence: emergent classicality from information bottleneck

  Zhelun Zhang , Yi-Zhuang You

  Machine Learning: Science and Technology (1), 015051 (2024)

  We train a generative language model on the randomized local measurement data collected from Schrödinger's cat quantum state. We demonstrate that the classical reality emerges in the language model due to the information bottleneck: although our training data contains the full quantum information about Schrödinger's cat, a weak language model can only learn to capture the classical reality of the cat from the data. We identify the quantum–classical boundary in terms of both the size of the quantum system and the information processing power of the classical intelligent agent, which indicates that a stronger agent can realize more quantum nature in the environmental noise surrounding the quantum system. Our approach opens up a new avenue for using the big data generated on noisy intermediate-scale quantum devices to train generative models for representation learning of quantum operators, which …

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  High-order time-reversal symmetry breaking normal state

  Meng Zeng , Lun-Hui Hu , Hong-Ye Hu , Yi-Zhuang You , Congjun Wu

  Science China Physics, Mechanics & Astronomy (3), 237411 (2024)

  Spontaneous time-reversal symmetry breaking plays an important role in studying strongly correlated unconventional superconductors. When two superconducting gap functions with different symmetries compete, the relative phase channel ( θ − ≡ θ 1 − θ 2 ) exhibits an Ising-type Z 2 symmetry due to the second order Josephson coupling, where θ 1,2 are the phases of two gap functions. In contrast, the U (1) symmetry in the channel of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\theta _ + } \equiv {{{\theta _1} + {\theta _2}} \over 2}$$\end{document} is intact. The phase locking, i.e., ordering of θ − , can take place in the phase fluctuation regime before the onset of superconductivity, i.e., when θ …

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  Measurement-induced criticality is tomographically optimal

  Ahmed A Akhtar , Hong-Ye Hu , Yi-Zhuang You

  Physical Review B (9), 094209 (2024)

  We develop a classical shadow tomography protocol utilizing the randomized measurement scheme based on hybrid quantum circuits, which consist of layers of two-qubit random Clifford unitary gates mixed with single-qubit random Pauli measurements. Unlike conventional protocols that perform all measurements by the end of unitary evolutions, our protocol allows measurements to occur at any space-time position throughout the quantum evolution. We provide a universal classical post-processing strategy to approximately reconstruct the original quantum state from intermittent measurement outcomes given the corresponding random circuit realizations over repeated experiments. We investigated the sample complexity for estimating different observables at different measurement rates of the hybrid quantum circuits. Our result shows that the sample complexity has an optimal scaling at the critical measurement …

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  Quantum magnetism in Wannier-obstructed Mott insulators

  Xiaoyang Huang , Taige Wang , Shang Liu , Hong-Ye Hu , Yi-Zhuang You

  Crystals (2), 176 (2024)

  We develop a strong coupling approach towards quantum magnetism in Mott insulators for Wannier-obstructed bands. Despite the lack of Wannier orbitals, electrons can still singly occupy a set of exponentially localized but nonorthogonal orbitals to minimize the repulsive interaction energy. We develop a systematic method to establish an effective spin model from the electron Hamiltonian using a diagrammatic approach. The nonorthogonality of the Mott basis gives rise to multiple new channels of spin-exchange (or permutation) interactions beyond Hartree–Fock and superexchange terms. We apply this approach to a Kagome lattice model of interacting electrons in Wannier-obstructed bands (including both Chern bands and fragile topological bands). Due to the orbital nonorthogonality, as parameterized by the nearest-neighbor orbital overlap g , this model exhibits stable ferromagnetism up to a finite bandwidth W∼Ug, where U is the interaction strength. This provides an explanation for the experimentally observed robust ferromagnetism in Wannier-obstructed bands. The effective spin model constructed through our approach also opens up the possibility for frustrated quantum magnetism around the ferromagnet-antiferromagnet crossover in Wannier-obstructed bands.

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  Definition and classification of Fermi surface anomalies

  Da-Chuan Lu , Juven Wang , Yi-Zhuang You

  Physical Review B (4), 045123 (2024)

  We propose that the Fermi surface anomaly of symmetry group in any dimension is universally classified by -symmetric interacting fermionic symmetry-protected topological (SPT) phases in -dimensional spacetime. The argument is based on the perspective that the gapless fermions on the Fermi surface can be viewed as the topological boundary modes of Chern insulators in the phase space (position-momentum space). Given the noncommutative nature of the phase-space coordinates, we show that the momentum space dimensions should be counted as negative dimensions for SPT classification purposes. Therefore, the classification of phase-space Chern insulators (or, more generally fermionic SPT phases) always reduces to a -dimensional problem, which can then be answered by the cobordism approach. In addition to the codimension-1 Fermi surface case, we also discuss the codimension …

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  CRT Fractionalization, Fermions, and Mod 8 Periodicity

  Zheyan Wan , Juven Wang , Shing-Tung Yau , Yi-Zhuang You

  ArXiv Preprint arXiv:2312.17126 (2023)

  Charge conjugation (C), mirror reflection (R), time reversal (T), and fermion parity are basic discrete spacetime and internal symmetries of the Dirac fermions. In this article, we determine the group, called the C-R-T fractionalization, which is a group extension of by the fermion parity , and its extension class in all spacetime dimensions , for a single-particle fermion theory. For Dirac fermions, with the canonical CRT symmetry , the C-R-T fractionalization has two possibilities that only depend on spacetime dimensions modulo 8, which are order-16 nonabelian groups, including the famous Pauli group. For Majorana fermions, we determine the R-T fractionalization in all spacetime dimensions , which is an order-8 abelian or nonabelian group. For Weyl fermions, we determine the C or T fractionalization in all even spacetime dimensions , which is an order-4 abelian group. For Majorana-Weyl fermions, we only have an order-2 group. We discuss how the Dirac and Majorana mass terms break the symmetries C, R, or T. We study the domain wall dimensional reduction of the fermions and their C-R-T fractionalization: from -dim Dirac to -dim Dirac or Weyl; and from -dim Majorana to -dim Majorana or Majorana-Weyl.

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  Probing the edge states of Chern insulators using microwave impedance microscopy

  Taige Wang , Chen Wu , Masataka Mogi , Minoru Kawamura , Yoshinori Tokura , Zhi-Xun Shen , Yi–Zhuang You , Monica T Allen

  Physical Review B (23), 235432 (2023)

  Microwave impedance microscopy (MIM) has been utilized to directly visualize topological edge states in many quantum materials. While the microwave response for conventional metals and insulators can be accurately quantified using simple lumped-element circuits, whose applicability to more exotic quantum systems remain limited. In this work, we present a general theoretical framework of the MIM response of arbitrary quantum materials. Applying it to topological edge states in a Chern insulator predicts an enhanced MIM response at the crystal boundaries due to collective edge magnetoplasmon (EMP) excitations. The unique resonance frequency of these plasmonic modes allows one to disentangle the signatures of topological versus trivial edge states. To benchmark our analytical predictions, we experimentally probe the MIM response of quantum anomalous Hall edge states in a Cr-doped …

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  OMNIINPUT: A Model-centric Evaluation Framework through Output Distribution

  Weitang Liu , Ying Wai Li , Tianle Wang , Yi-Zhuang You , Jingbo Shang

  ArXiv Preprint arXiv:2312.03291 (2023)

  We propose a novel model-centric evaluation framework, OmniInput, to evaluate the quality of an AI/ML model's predictions on all possible inputs (including human-unrecognizable ones), which is crucial for AI safety and reliability. Unlike traditional data-centric evaluation based on pre-defined test sets, the test set in OmniInput is self-constructed by the model itself and the model quality is evaluated by investigating its output distribution. We employ an efficient sampler to obtain representative inputs and the output distribution of the trained model, which, after selective annotation, can be used to estimate the model's precision and recall at different output values and a comprehensive precision-recall curve. Our experiments demonstrate that OmniInput enables a more fine-grained comparison between models, especially when their performance is almost the same on pre-defined datasets, leading to new findings and insights for how to train more robust, generalizable models.

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  Evaluation of human-model prediction difference on the Internet Scale of Data

  Weitang Liu , Ying Wai Li , Yuelei Li , Zihan Wang , Yi-Zhuang You , Jingbo Shang

  ArXiv E-prints, arXiv: 2312.03291 (2023)

  Evaluating models on datasets often fails to capture their behavior when faced with unexpected and diverse types of inputs. It would be beneficial if we could evaluate the difference between human annotation and model prediction for an internet number of inputs, or more generally, for an input space that enumeration is computationally impractical. Traditional model evaluation methods rely on precision and recall (PR) as metrics, which are typically estimated by comparing human annotations with model predictions on a specific dataset. This is feasible because enumerating thousands of test inputs is manageable. However, estimating PR across a large input space is challenging because enumeration becomes computationally infeasible. We propose OmniInput, a novel approach to evaluate and compare NNs by the PR of an input space. OmniInput is distinctive from previous works as its estimated PR reflects the …

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  Fermi surface symmetric mass generation: a quantum Monte-Carlo study

  Wei-Xuan Chang , Sibo Guo , Yi-Zhuang You , Zi-Xiang Li

  ArXiv Preprint arXiv:2311.09970 (2023)

  The symmetric mass generation (SMG) phase is an insulator in which a single-particle gap is intrinsically opened by the interaction, without involving symmetry spontaneously breaking or topological order. Here, we perform unbiased quantum Monte-Carlo simulation and systematically investigate a bilayer fermionic model hosting Fermi surface SMG in the strongly interacting regime. With increasing interaction strength, the model undergoes a quantum phase transition from an exciton insulator to an SMG phase, belonging to the (2+1)-dimensional O(4) universality class. We access the spectral properties of the SMG phase, resembling a Mott insulating phase with relatively flat dispersion and pronounced spectral broadening. The dispersion of Green's function zeros is extracted from spectral function, featuring a surface at zero frequency precisely located at the original non-interacting Fermi surface, which constitutes a hallmark of the Fermi surface SMG phase. The bilayer model we study is potentially relevant to the newly discovered high- superconductor . Our results in SMG phase qualitatively capture the salient features of spectral function unveiled in recent ARPES experiments, shedding new insight on the underlying physics of .

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  Green's function zeros in Fermi surface symmetric mass generation

  Da-Chuan Lu , Meng Zeng , Yi-Zhuang You

  Physical Review B (20), 205117 (2023)

  The Fermi surface symmetric mass generation (SMG) is an intrinsically interaction-driven mechanism that opens an excitation gap on the Fermi surface without invoking symmetry-breaking or topological order. We explore this phenomenon within a bilayer square lattice model of spin-1/2 fermions, where the system can be tuned from a metallic Fermi liquid phase to a strongly interacting SMG insulator phase by an interlayer spin-spin interaction. The SMG insulator preserves all symmetries and has no mean-field interpretation at the single-particle level. It is characterized by zeros in the fermion Green's function, which encapsulate the same Fermi volume in momentum space as the original Fermi surface, a feature mandated by the Luttinger theorem. Utilizing both numerical and field-theoretical methods, we provide compelling evidence for these Green's function zeros across both strong and weak coupling regimes of …

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  Machine learning renormalization group for statistical physics

  Wanda Hou , Yi-Zhuang You

  Machine Learning: Science and Technology (4), 045010 (2023)

  We develop a machine-learning renormalization group (MLRG) algorithm to explore and analyze many-body lattice models in statistical physics. Using the representation learning capability of generative modeling, MLRG automatically learns the optimal renormalization group (RG) transformations from self-generated spin configurations and formulates RG equations without human supervision. The algorithm does not focus on simulating any particular lattice model but broadly explores all possible models compatible with the internal and lattice symmetries given the on-site symmetry representation. It can uncover the RG monotone that governs the RG flow, assuming a strong form of the c-theorem. This enables several downstream tasks, including unsupervised classification of phases, automatic location of phase transitions or critical points, controlled estimation of critical exponents, and operator scaling dimensions …

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  Symmetric mass generation of Kähler-Dirac fermions from the perspective of symmetry-protected topological phases

  Yuxuan Guo , Yi-Zhuang You

  Physical Review B (11), 115139 (2023)

  The Kähler-Dirac fermion, recognized as an elegant geometric approach, offers an alternative to traditional representations of relativistic fermions. Recent studies have demonstrated that symmetric mass generation (SMG) can precisely occur with two copies of Kähler-Dirac fermions across any space-time dimensions. This conclusion stems from the study of anomaly cancellation within the fermion system. Our research provides an alternative understanding of this phenomenon from a condensed matter perspective, by associating the interacting Kähler-Dirac fermion with the boundary of bosonic symmetry-protected topological (SPT) phases. We show that the low-energy bosonic fluctuations in a single copy of the Kähler-Dirac fermion can be mapped to the boundary modes of a -classified bosonic SPT state, protected by an inversion symmetry universally across all dimensions. This implies that two copies of …

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  Variational Monte Carlo study of symmetric mass generation in a bilayer honeycomb lattice model

  Wanda Hou , Yi-Zhuang You

  Physical Review B (12), 125130 (2023)

  We investigate a bilayer honeycomb lattice model of spin-1/2 fermions at half-filling with local Heisenberg coupling of fermion spins across the two layers. Using variational Monte Carlo (VMC) simulation, we demonstrate that the system undergoes a direct transition from a Dirac semimetal phase to a symmetric gapped phase, known as symmetric mass generation (SMG), as the Heisenberg coupling strength is increased. The transition does not involve spontaneous symmetry breaking or topological order and has been proposed as an example of the fermionic deconfined quantum critical point (fDQCP). Our simulation shows that a fermionic parton bilinear mass opens at the transition point while all symmetries are still preserved thanks to the quantum fluctuations introduced by the correlation factor in the variational wave function. From the simulation data, we extract the critical exponent and the fermion …

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  Superconductivity from Doping Symmetric Mass Generation Insulators: Application to La_3Ni_2O_7 under Pressure

  Da-Chuan Lu , Miao Li , Zhao-Yi Zeng , Wanda Hou , Juven Wang , Fan Yang , Yi-Zhuang You

  ArXiv Preprint arXiv:2308.11195 (2023)

  We investigate the bilayer nickelates as a platform to realize the symmetric mass generation (SMG) insulator, a featureless Mott insulator that arises due to the Lieb-Schultz-Mattis (LSM) anomaly cancellation in bilayer spin-1/2 lattice systems. Through a single-orbital bilayer square lattice model involving intralayer hopping and interlayer superexchange interaction , we demonstrate the emergence of high-temperature superconductivity (SC) upon doping the SMG insulator. The SC phase features -wave interlayer spin-singlet pairing and exhibits a crossover between the BCS and BEC limits by tuning the ratio. We estimate the SC transition temperature from both the weak and strong coupling limits at the mean-field level. Our findings offer insights into the experimentally observed decrease in with pressure and the strange metal behavior above . Additionally, we propose that both Ni and orbitals can exhibit superconductivity in La Ni O under pressure, but their should vary in opposite ways under doping. This characteristic difference suggests a potential experimental pathway to identify which electronic orbital plays the principal role in the formation of superconductivity in this system.

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  Gradient-based wang-landau algorithm: A novel sampler for output distribution of neural networks over the input space

  Weitang Liu , Yi-Zhuang You , Ying Wai Li , Jingbo Shang

  International Conference on Machine Learning, 22338-22351 (2023)

  The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering in-sights toward a more comprehensive NN under-standing. Exhaustive enumeration or traditional Monte Carlo methods for the entire input space can exhibit impractical sampling time, especially for high-dimensional inputs. To make such difficult sampling computationally feasible, in this paper, we propose a novel Gradient-based Wang-Landau (GWL) sampler. We first draw the connection between the output distribution of a NN and the density of states (DOS) of a physical system. Then, we renovate the classic sampler for the DOS problem, Wang-Landau algorithm, by re-placing its random proposals with gradient-based Monte Carlo proposals. This way, our GWL sampler investigates the under-explored subsets of the input space much more efficiently. Extensive experiments have verified the accuracy of the output distribution generated by GWL and also showcased several interesting findings-for example, in a binary image classification task, both CNN and ResNet mapped the majority of human unrecognizable images to very negative logit values.

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  Scalable and flexible classical shadow tomography with tensor networks

  Ahmed A Akhtar , Hong-Ye Hu , Yi-Zhuang You

  Quantum, 1026 (2023)

  Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of a quantum state with few measurements. Two classical shadow protocols have been extensively studied in the literature: the single-qubit (local) Pauli measurement, which is well suited for predicting local operators but inefficient for large operators; and the global Clifford measurement, which is efficient for low-rank operators but infeasible on near-term quantum devices due to the extensive gate overhead. In this work, we demonstrate a scalable classical shadow tomography approach for generic randomized measurements implemented with finite-depth local Clifford random unitary circuits, which interpolates between the limits of Pauli and Clifford measurements. The method combines the recently proposed locally-scrambled classical shadow tomography framework with tensor network techniques to achieve scalability for computing the classical shadow reconstruction map and evaluating various physical properties. The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead and is friendly to noisy intermediate-scale quantum (NISQ) devices. We show that the shallow-circuit measurement protocol provides immediate, exponential advantages over the Pauli measurement protocol for predicting quasi-local operators. It also enables a more efficient fidelity estimation compared to the Pauli measurement.

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  Fermi surface symmetric mass generation

  Da-Chuan Lu , Meng Zeng , Juven Wang , Yi-Zhuang You

  Physical Review B (19), 195133 (2023)

  Symmetric mass generation (SMG) is a mechanism to give gapless fermions a mass gap by nonperturbative interactions without generating any fermion bilinear condensation. The previous studies of SMG have been limited to Dirac/Weyl/Majorana fermions with zero Fermi volume in the free fermion limit. In this paper, we generalize the concept of SMG to Fermi liquid (FL) with a finite Fermi volume and discuss how to gap out the Fermi surfaces (FSs) by interactions without breaking the U(1) loop group symmetry or developing topological orders. We provide examples of FS SMG in both -dimensional and -dimensional FL systems when several FSs together cancel the FS anomaly. However, the U(1) loop group symmetry in these cases is still restrictive enough to rule out all possible fermion bilinear gapping terms, such that a nonperturbative interaction mechanism is the only way to gap out the FSs …

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  Classical shadow tomography with locally scrambled quantum dynamics

  Hong-Ye Hu , Soonwon Choi , Yi-Zhuang You

  Physical Review Research (2), 023027 (2023)

  We generalize the classical shadow tomography scheme to a broad class of finite-depth or finite-time local unitary ensembles, known as locally scrambled quantum dynamics, where the unitary ensemble is invariant under local-basis transformations. In this case, the reconstruction map for the classical shadow tomography depends only on the average entanglement feature of classical snapshots. We provide an unbiased estimator of the quantum state as a linear combination of reduced classical snapshots in all subsystems, where the combination coefficients are solely determined by the entanglement feature. We also bound the number of experimental measurements required for the tomography scheme, so-called sample complexity, by formulating the operator shadow norm in the entanglement feature formalism. We numerically demonstrate our approach for finite-depth local unitary circuits and finite-time local …

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  Categorical representation learning and RG flow operators for algorithmic classifiers

  Artan Sheshmani , Yi-Zhuang You , Wenbo Fu , Ahmadreza Azizi

  Machine Learning: Science and Technology (1), 015012 (2023)

  Following the earlier formalism of the categorical representation learning, we discuss the construction of the'RG-flow-based categorifier'. Borrowing ideas from the theory of renormalization group (RG) flows in quantum field theory, holographic duality, and hyperbolic geometry and combining them with neural ordinary differential equation techniques, we construct a new algorithmic natural language processing architecture, called the RG-flow categorifier or for short the RG categorifier, which is capable of data classification and generation in all layers. We apply our algorithmic platform to biomedical data sets and show its performance in the field of sequence-to-function mapping. In particular, we apply the RG categorifier to particular genomic sequences of flu viruses and show how our technology is capable of extracting the information from given genomic sequences, finding their hidden symmetries and dominant …

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  Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: A renormalization group analysis

  Da-Chuan Lu , Taige Wang , Shubhayu Chatterjee , Yi-Zhuang You

  Physical Review B (15), 155115 (2022)

  Motivated by recent experimental observations of correlated metallic phases and superconductivity in rhombohedral trilayer graphene (RTG), we perform an unbiased study of electronic ordering instabilities in hole-doped RTG. Specifically, we focus on electronic states energetically proximate to Van Hove singularities (VHSs), where a large density of states promotes different interaction-induced symmetry-breaking electronic orders. To resolve the Fermi surface near VHSs, we construct a fermionic hot-spot model and demonstrate that a perpendicular electric field can tune different nesting structures of the Fermi surface. Subsequently, we apply a renormalization group analysis to describe the low-energy phase diagrams of our model under both short-range repulsive interactions as well as realistic (long-range) Coulomb interactions. Our analysis shows instabilities towards either intervalley coherent metallic phases or …

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  Cobordism and deformation class of the standard model

  Juven Wang , Zheyan Wan , Yi-Zhuang You

  Physical Review D (4), L041701 (2022)

  ’t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry (including spacetime and internal symmetries) in a spacetime are known to be classified by a cobordism group , whose group generator is a cobordism invariant written as an invertible topological field theory (iTFT) with a partition function . It has recently been proposed that the deformation class of QFTs is specified by its symmetry and an iTFT . Seemingly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. In this work, we ask which cobordism class and deformation class control the 4d standard model (SM) of ungauged or gauged group for , 2, 3, 6 with a continuous or discrete baryon minus lepton -like symmetry. We show that the answer contains some combination of 5d iTFTs; two classes associated with and 4d perturbative local anomalies, a …

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  RG-Flow: A hierarchical and explainable flow model based on renormalization group and sparse prior

  Hong-Ye Hu , Dian Wu , Yi-Zhuang You , Bruno Olshausen , Yubei Chen

  Machine Learning: Science and Technology (3), 035009 (2022)

  Flow-based generative models have become an important class of unsupervised learning approaches. In this work, we incorporate the key ideas of renormalization group (RG) and sparse prior distribution to design a hierarchical flow-based generative model, RG-Flow, which can separate information at different scales of images and extract disentangled representations at each scale. We demonstrate our method on synthetic multi-scale image datasets and the CelebA dataset, showing that the disentangled representations enable semantic manipulation and style mixing of the images at different scales. To visualize the latent representations, we introduce receptive fields for flow-based models and show that the receptive fields of RG-Flow are similar to those of convolutional neural networks. In addition, we replace the widely adopted isotropic Gaussian prior distribution by the sparse Laplacian distribution to further …

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  Fluctuation of Chern Numbers in a Parametric Random Matrix Model

  Hung-Hwa Lin , Wei-Ting Kuo , Daniel P Arovas , Yi-Zhuang You

  ArXiv Preprint arXiv:2207.12562 (2022)

  Band-touching Weyl points in Weyl semimetals give rise to many novel characteristics, one of which the presence of surface Fermi-arc states that is topologically protected. The number of such states can be computed by the Chern numbers at different momentum slices, which fluctuates with changing momentum and depends on the distribution of Weyl points in the Brillouin zone. For realistic systems, it may be difficult to locate the momenta at which these Weyl points and Fermi-arc states appear. Therefore, we extend the analysis of a parametric random matrix model proposed by Walker and Wilkinson to find the statistics of their distributions. Our numerical data shows that Weyl points with opposite polarities are short range correlated, and the Chern number fluctuation only grows linearly for a limited momentum difference before it saturates. We also find that the saturation value scales with the total number of bands. We then compute the short-range correlation length from perturbation theory, and derive the dependence of the Chern number fluctuation on the momentum difference, showing that the saturation results from the short-range correlation.

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  Symmetric mass generation

  Juven Wang , Yi-Zhuang You

  Symmetry (7), 1475 (2022)

  The most well-known mechanism for fermions to acquire a mass is the Nambu–Goldstone–Anderson–Higgs mechanism, i.e., after a spontaneous symmetry breaking, a bosonic field that couples to the fermion mass term condenses, which grants a mass gap for the fermionic excitation. In the last few years, it was gradually understood that there is a new mechanism of mass generation for fermions without involving any symmetry breaking within an anomaly-free symmetry group, also applicable to chiral fermions with anomaly-free chiral symmetries. This new mechanism is generally referred to as the symmetric mass generation (SMG). It is realized that the SMG has deep connections with interacting topological insulator/superconductors, symmetry-protected topological states, perturbative local and non-perturbative global anomaly cancellations, and deconfined quantum criticality. It has strong implications for the lattice regularization of chiral gauge theories. This article defines the SMG, summarizes the current numerical results, introduces an unifying theoretical framework (including the parton-Higgs and the s-confinement mechanisms, as well as the symmetry-extension construction), and presents an overview of various features and applications of SMG.

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  Proton stability: From the standard model to beyond grand unification

  Juven Wang , Zheyan Wan , Yi-Zhuang You

  Physical Review D (2), 025016 (2022)

  A proton is known for its longevity, but what is its lifetime? While many grand unified Theories predict the proton decay with a finite lifetime, we show that the Standard Model (SM) and some versions of ultraunification (which replace sterile neutrinos with new exotic gapped/gapless sectors, e.g., topological or conformal field theory under global anomaly cancellation constraints) with a discrete baryon plus lepton symmetry permit a stable proton. For the 4D SM with Lie group GSMq≡SU(3)×SU(2)×U(1)Y˜Zq of , 2, 3, 6 and families of 15 or 16 Weyl fermions, in addition to the continuous baryon minus lepton symmetry, there is also a compatible discrete baryon plus lepton symmetry. The is discrete due to the Adler-Bell-Jackiw anomaly under the BPST SU(2) instanton. Although both and symmetries are anomaly free under the dynamically gauged , it is important to check whether they have mixed …

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  Gauge enhanced quantum criticality beyond the standard model

  Juven Wang , Yi-Zhuang You

  Physical Review D (2), 025013 (2022)

  Standard lore ritualizes our quantum vacuum in the four-dimensional spacetime (4D) governed by one of the candidate Standard Models (SMs), while lifting towards some grand unification-like structure (GUT) at higher energy scales. In contrast, in our work, we introduce an alternative view that the SM is a low energy quantum vacuum arising from various neighbor vacua competition in an immense quantum phase diagram. In general, we can regard the SM arising near the gapless quantum criticality (either critical points or critical regions) between the competing neighbor vacua. In particular detail, we demonstrate how the SM with 16n Weyl fermions arises near the quantum criticality between the GUT competition of Georgi-Glashow and Pati-Salam . We propose two enveloping toy models. Model I is the conventional GUT with a Spin(10) gauge group plus GUT-Higgs …

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  Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model

  Meng Zeng , Zheng Zhu , Juven Wang , Yi-Zhuang You

  Physical Review Letters (18), 185301 (2022)

  Lattice regularization of chiral fermions has been a long-standing problem in physics. In this Letter, we present the density matrix renormalization group simulation of the 3-4-5-0 model of chiral fermions with an anomaly-free chiral U(1) symmetry, which contains two left-moving and two right-moving fermions carrying U(1) charges 3,4 and 5,0, respectively. Following the Wang-Wen chiral fermion model, we realize the chiral fermions and their mirror partners on the opposite boundaries of a thin strip of lattice model of multilayer Chern insulator, whose finite width implies the quantum system is effectively . By introducing two sets of carefully designed six-fermion local interactions to the mirror sector only, we demonstrate that the mirror fermions can be gapped out by the interaction beyond a critical strength without breaking the chiral U(1) symmetry, via the symmetric mass generation mechanism …

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  Kohn-Luttinger superconductivity and intervalley coherence in rhombohedral trilayer graphene

  Yi-Zhuang You , Ashvin Vishwanath

  Physical Review B (13), 134524 (2022)

  Motivated by recent experiments on ABC-stacked rhombohedral trilayer graphene (RTG), which observed spin-valley symmetry breaking and superconductivity, we study instabilities of the RTG metallic state to symmetry-breaking orders. We find that interactions select the intervalley coherent order (IVC) as the preferred ordering channel over a wide range, whose theoretically determined phase boundaries agree well with experiments on both the hole- and electron-doped sides. The Fermi surfaces near van Hove singularities admit partial nesting between valleys, which promotes both intervalley superconductivity and IVC fluctuations. We investigate the interplay between these fluctuations and the Hunds (intervalley spin) interaction using a renormalization group approach. For antiferromagnetic Hund's coupling, intervalley pairing appears in the spin-singlet channel with enhanced that scales with the dimensionless …

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  Logical shadow tomography: Efficient estimation of error-mitigated observables

  Hong-Ye Hu , Ryan LaRose , Yi-Zhuang You , Eleanor Rieffel , Zhihui Wang

  ArXiv Preprint arXiv:2203.07263 (2022)

  We introduce a technique to estimate error-mitigated expectation values on noisy quantum computers. Our technique performs shadow tomography on a logical state to produce a memory-efficient classical reconstruction of the noisy density matrix. Using efficient classical post-processing, one can mitigate errors by projecting a general nonlinear function of the noisy density matrix into the codespace. The subspace expansion and virtual distillation can be viewed as special cases of the new framekwork. We show our method is favorable in the quantum and classical resources overhead. Relative to subspace expansion which requires samples to estimate a logical Pauli observable with error correction code, our technique requires only samples. Relative to virtual distillation, our technique can compute powers of the density matrix without additional copies of quantum states or quantum memory. We present numerical evidence using logical states encoded with up to sixty physical qubits and show fast convergence to error-free expectation values with only samples under 1% depolarizing noise.

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  Ultrafast coherence delocalization in real space simulated by polaritons

  Bo Xiang , Zimo Yang , Yi‐Zhuang You , Wei Xiong

  Advanced Optical Materials (5), 2102237 (2022)

  Coherence delocalization has been investigated on a coupled‐cavity molecular polariton platform in time, frequency, and spatial domains, enabled by ultrafast two‐dimensional infrared hyperspectral imaging. Unidirectional coherence delocalization (coherence prepared in one cavity transferred to another cavity) has been observed in frequency and real space. This directionality is enabled by the dissipation of delocalized photon from high‐energy to low‐energy modes, described by Lindblad dynamics. Further experiments show that when coherences are directly prepared between polaritons from different cavities, only energetically nearby polaritons can form coherences that survive the long‐range environmental fluctuation. Together with the Lindblad dynamics, this result implies that coherences delocalize through a one‐step mechanism where photons transfer from one cavity to another, shedding light to …

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  Deconfined quantum criticality among grand unified theories

  Yi-Zhuang You , Juven Wang

  A Festschrift in Honor of the CN Yang Centenary: Scientific Papers, 367-383 (2022)

  This article reviews the recent developments in applying the idea of deconfined quantum criticality in condensed matter physics to understand quantum phase transitions among grand unified theories in high energy physics. In particular, dictated by a nontrivial mod 2 class nonperturbative global gauge-gravitational anomaly, there can be a deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — not only the Standard Model occurs as a neighbor phase, but also beyond the Standard Model phenomena (such as dark gauge force and fragmentary partons) occur near the critical region.

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  Hamiltonian-driven shadow tomography of quantum states

  Hong-Ye Hu , Yi-Zhuang You

  Physical Review Research (1), 013054 (2022)

  Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. Facing the challenge of realizing deep unitary circuits on near-term quantum devices, we explore the scenario in which the unitary channel can be shallow and is generated by a quantum chaotic Hamiltonian via time evolution. We provide an unbiased estimator of the density matrix for all ranges of the evolution time. We analyze the sample complexity of the Hamiltonian-driven shadow tomography. For Pauli observables, we find that it can be more efficient than the unitary-2-design-based shadow tomography in a sequence of intermediate time windows that range from an order-1 scrambling time to a timescale of , given the Hilbert space dimension …

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  Categorical representation learning: morphism is all you need

  Artan Sheshmani , Yi-Zhuang You

  Machine Learning: Science and Technology (1), 015016 (2021)

  We provide a construction for categorical representation learning and introduce the foundations of'categorifier'. The central theme in representation learning is the idea of everything to vector. Every object in a dataset

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  Machine learning statistical gravity from multi-region entanglement entropy

  Jonathan Lam , Yi-Zhuang You

  Physical Review Research (4), 043199 (2021)

  The Ryu-Takayanagi formula directly connects quantum entanglement and geometry. Yet the assumption of static geometry lead to an exponentially small mutual information between far-separated disjoint regions, which does not hold in many systems such as free fermion conformal field theories. In this paper, we proposed a microscopic model by superimposing entanglement features of an ensemble of random tensor networks of different bond dimensions, which can be mapped to a statistical gravity model consisting of a massive scalar field on a fluctuating background geometry. We propose a machine-learning algorithm that recovers the underlying geometry fluctuation from multi-region entanglement entropy data by modeling the bulk geometry distribution via a generative neural network. To demonstrate its effectiveness, we tested the model on a free fermion system and showed mutual information can be …

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  Self-duality protected multicriticality in deconfined quantum phase transitions

  Da-Chuan Lu , Cenke Xu , Yi-Zhuang You

  Physical Review B (20), 205142 (2021)

  Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multicriticalities. This work investigates a description of the deconfined quantum criticality, the , as an example of self-dual theories, and its multicritical behavior under perturbative deformations. The multicriticality is described by the theory with Gross-Neveu couplings and falls in a different universality class than the standard deconfined quantum criticality. We systematically calculate the scaling dimensions of various operators in the 3D quantum electrodynamics with the Chern-Simons term and Gross-Neveu couplings by the large- renormalization group analysis. Specifically, we find certain Drelativistic four-fermion interactions which correspond to the dimer-dimer interactions in the lattice model will drive the …

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  Decoherent quench dynamics across quantum phase transitions

  Wei-Ting Kuo , Daniel P Arovas , Smitha Vishveshwara , Yi-Zhuang You

  SciPost Physics (4), 084 (2021)

  We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. We generalize the well-studied universal Kibble-Zurek behavior for linear temporal drive across the critical point. We identify a strong decoherence regime wherein the decoherence time is shorter than the standard correlation time, which varies as the inverse gap above the groundstate. In this regime, we find that the freeze-out time for when the system falls out of equilibrium and the associated freeze-out length show power-law scaling with respect to the quench rate , where the exponents depend on the correlation length exponent and the dynamical exponent associated with the transition. The universal exponents differ from those of standard Kibble-Zurek scaling. We explicitly demonstrate this scaling behavior in the instance of a topological transition in a Chern insulator system. We show that the freeze-out time scale can be probed from the relaxation of the Hall conductivity. Furthermore, on introducing disorder to break translational invariance, we demonstrate how quenching results in regions of imbalanced excitation density characterized by an emergent length scale which also shows universal scaling. We perform numerical simulations to confirm our analytical predictions and corroborate the scaling arguments that we postulate as universal to a host of systems.

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  Strong correlation between superconductivity and ferromagnetism in an Fe-chalcogenide superconductor

  Nathan J McLaughlin , Hailong Wang , Mengqi Huang , Eric Lee-Wong , Lunhui Hu , Hanyi Lu , Gerald Q Yan , Genda Gu , Congjun Wu , Yi-Zhuang You , Chunhui Rita Du

  Nano Letters (17), 7277-7283 (2021)

  The interplay among topology, superconductivity, and magnetism promises to bring a plethora of exotic and unintuitive behaviors in emergent quantum materials. The family of Fe-chalcogenide superconductors FeTe x Se 1– x are directly relevant in this context due to their intrinsic topological band structure, high-temperature superconductivity, and unconventional pairing symmetry. Despite enormous promise and expectation, the local magnetic properties of FeTe x Se 1– x remain largely unexplored, which prevents a comprehensive understanding of their underlying material properties. Exploiting nitrogen vacancy (NV) centers in diamond, here we report nanoscale quantum sensing and imaging of magnetic flux generated by exfoliated FeTe x Se 1– x flakes, demonstrating strong correlation between superconductivity and ferromagnetism in FeTe x Se 1– x . The coexistence of superconductivity and ferromagnetism in an …

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  Neural ordinary differential equation and holographic quantum chromodynamics

  Koji Hashimoto , Hong-Ye Hu , Yi-Zhuang You

  Machine Learning: Science and Technology (3), 035011 (2021)

  The neural ordinary differential equation (neural ODE) is a novel machine learning architecture whose weights are smooth functions of the continuous depth. We apply the neural ODE to holographic QCD by regarding the weight functions as a bulk metric, and train the machine with lattice QCD data of chiral condensate at finite temperature. The machine finds consistent bulk geometry at various values of temperature and discovers the emergent black hole horizon in the holographic bulk automatically. The holographic Wilson loops calculated with the emergent machine-learned bulk spacetime have consistent temperature dependence of confinement and Debye-screening behavior. In machine learning models with physically interpretable weights, the neural ODE frees us from discretization artifact leading to difficult ingenuity of hyperparameters, and improves numerical accuracy to make the model more trustworthy.

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  Self-organized error correction in random unitary circuits with measurement

  Ruihua Fan , Sagar Vijay , Ashvin Vishwanath , Yi-Zhuang You

  Physical Review B (17), 174309 (2021)

  Random measurements have been shown to induce a phase transition in an extended quantum system evolving under chaotic unitary dynamics, when the strength of measurements exceeds a threshold value. Below this threshold, a steady state with a subthermal volume law entanglement emerges, which is resistant to the disentangling action of measurements, suggesting a connection to quantum error-correcting codes. We quantify these notions by identifying a power-law decay of the mutual information in the volume-law-entangled phase, between a qudit located a distance from the boundary of a region , and the complement , which implies that a measurement of this qudit will retrieve very little information about . We also find a universal logarithmic contribution to the volume law entanglement entropy which is intimately related to the first observation. We obtain these results by relating the …

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  Topological and symmetry-enriched random quantum critical points

  Carlos M Duque , Hong-Ye Hu , Yi-Zhuang You , Vedika Khemani , Ruben Verresen , Romain Vasseur

  Physical Review B (10), L100207 (2021)

  We study how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. These are the disordered analogs of gapless topological phases. Using real-space and density matrix renormalization group approaches, we analyze the boundary and bulk critical behavior of such symmetry-enriched random quantum spin chains. We uncover a new class of symmetry-enriched infinite randomness fixed points: while local bulk properties are indistinguishable from conventional random singlet phases, nonlocal observables, and boundary critical behavior are controlled by a different renormalization group fixed point. We also illustrate how such new quantum critical points emerge naturally in Floquet systems.

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  Machine learning identification of impurities in the STM images

  Ce Wang , Haiwei Li , Zhenqi Hao , Xintong Li , Changwei Zou , Peng Cai , Yayu Wang , Yi-Zhuang You , Hui Zhai

  Chinese Physics B (11), 116805 (2020)

  We train a neural network to identify impurities in the experimental images obtained by the scanning tunneling microscope (STM) measurements. The neural network is first trained with a large number of simulated data and then the trained neural network is applied to identify a set of experimental images taken at different voltages. We use the convolutional neural network to extract features from the images and also implement the attention mechanism to capture the correlations between images taken at different voltages. We note that the simulated data can capture the universal Friedel oscillation but cannot properly describe the non-universal physics short-range physics nearby an impurity, as well as noises in the experimental data. And we emphasize that the key of this approach is to properly deal with these differences between simulated data and experimental data. Here we show that even by including …

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  Multiregion entanglement in locally scrambled quantum dynamics

  AA Akhtar , Yi-Zhuang You

  Physical Review B (13), 134203 (2020)

  We study the evolution of multiregion bipartite entanglement entropy under locally scrambled quantum dynamics. We show that the multiregion entanglement can significantly modify the growth of single-region entanglement, whose effect has been largely overlooked in the existing literature. We developed a theoretical framework, called the entanglement feature formalism, to organize all the multiregion entanglement systematically as a sign-free many-body state. We further propose a two-parameter matrix product state (MPS) ansatz to efficiently capture the exponentially many multiregion entanglement features. Using these tools, we are able to study the multiregion entanglement dynamics jointly and represent the evolution in the MPS parameter space. By comparing the dynamical constraints on the motion of entanglement cuts, we are able to identify different quantum dynamics models in a unifying entanglement …

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  Topological phase transition on the edge of two-dimensional Z2 topological order

  Wei-Qiang Chen , Chao-Ming Jian , Liang Kong , Yi-Zhuang You , Hao Zheng

  Physical Review B (4), 045139 (2020)

  The unified mathematical theory of gapped and gapless edges of two-dimensional (2d) topological orders was developed by two of the authors. According to this theory, the critical point of a purely edge topological phase transition of a 2d topological order can be mathematically characterized by an enriched fusion category. In this work, we provide a physical proof of this fact in a concrete example: the 2d topological order. In particular, we construct an enriched fusion category, which describes a gappable nonchiral gapless edge of the 2d topological order. Then, we use an explicit lattice model construction to realize a topological phase transition between the two well-known gapped edges of the 2d topological order, and show that all the ingredients of the above enriched fusion category can be realized explicitly in this lattice model.

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  Markovian entanglement dynamics under locally scrambled quantum evolution

  Wei-Ting Kuo , AA Akhtar , Daniel P Arovas , Yi-Zhuang You

  Physical Review B (22), 224202 (2020)

  We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely, the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under local (on-site) basis transformations. In this case, the average entanglement entropy follows a Markovian dynamics, such that the entanglement property of the future state can be inferred from the entanglement property of the unitary operator of the underlying quantum dynamics. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schrödinger equation, such that various tools developed in quantum many-body physics can be applied. The framework enables us to investigate a variety of …

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  Machine learning holographic mapping by neural network renormalization group

  Hong-Ye Hu , Shuo-Hui Li , Lei Wang , Yi-Zhuang You

  Physical Review Research (2), 023369 (2020)

  Exact holographic mapping (EHM) provides an explicit duality map between a conformal field theory (CFT) configuration and a massive field propagating on an emergent classical geometry. However, designing the optimal holographic mapping is challenging. Here we introduce the neural network renormalization group as a universal approach to design generic EHM for interacting field theories. Given a field theory action, we train a flow-based hierarchical deep generative neural network to reproduce the boundary field ensemble from uncorrelated bulk field fluctuations. In this way, the neural network develops the optimal renormalization-group transformations. Using the machine-designed EHM to map the CFT back to a bulk effective action, we determine the bulk geodesic distance from the residual mutual information. We have shown that the geometry measured in this way is the classical saddle-point geometry. We …

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  Information scrambling in quantum neural networks

  Huitao Shen , Pengfei Zhang , Yi-Zhuang You , Hui Zhai

  Physical Review Letters (20), 200504 (2020)

  The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information—a quantity recently developed to characterize information scrambling—to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases …

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  Measurement-induced criticality in random quantum circuits

  Chao-Ming Jian , Yi-Zhuang You , Romain Vasseur , Andreas WW Ludwig

  Physical Review B (10), 104302 (2020)

  We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of the entanglement entropies in such circuits onto a two-dimensional statistical-mechanics model. In this language, the area- to volume-law entanglement transition can be interpreted as an ordering transition in the statistical-mechanics model. We derive the general scaling properties of the entanglement entropies and mutual information near the transition using conformal invariance. We analyze in detail the limit of infinite on-site Hilbert space dimension in which the statistical-mechanics model maps onto percolation. In particular, we compute the exact value of the universal coefficient of the logarithm of subsystem size in the Rényi entropies for in this limit using relatively recent results for the conformal field …

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  Gauge enhanced quantum criticality and time reversal deconfined domain wall: SU (2) Yang-Mills dynamics with topological terms

  Juven Wang , Yi-Zhuang You , Yunqin Zheng

  Physical Review Research (1), 013189 (2020)

  We explore the low-energy dynamics of the four siblings of Lorentz symmetry enriched Yang-Mills theories with a theta term at in . Due to a mixed anomaly between time reversal symmetry and the one-form center symmetry, the low-energy dynamics cannot be symmetric trivially gapped. We focus on two possible scenarios: (1) time reversal symmetry is spontaneously broken by the two confining vacua and (2) a deconfined, gapless, and time reversal symmetric Maxwell gauge theory [e.g., spin liquid in condensed matter]. In the first scenario, we find that the antiunitary time reversal symmetry in the bulk induces a unitary symmetry on the domain wall between the two vacua. We discuss how the Lorentz symmetry and the unitary symmetry enrich the domain-wall topological field theory. In the second scenario, we relate the symmetry enrichments of the Yang-Mills to that of the Maxwell …

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  Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu2(BO3)2

  Jong Yeon Lee , Yi-Zhuang You , Subir Sachdev , Ashvin Vishwanath

  Physical Review X (4), 041037 (2019)

  We study a possible deconfined quantum phase transition in a realistic model of a two-dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. Using the infinite density matrix renormalization group (IDMRG) method, we verify the existence of an intermediate plaquette valence bond solid (PVBS) order, with twofold degeneracy, between the dimer and Néel ordered phases. We argue that the quantum phase transition between the Néel and PVBS orders may be described by a deconfined quantum critical point (DQCP) with an emergent O(4) symmetry . By analyzing the correlation length spectrum obtained from IDMRG, we provide evidence for the DQCP and emergent O(4) symmetry in the lattice model. Such a phase transition has been reported in the recent pressure-tuned experiments in the Shastry-Sutherland lattice material [Nat. Phys. 13, 962 (2017 …

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  Entanglement transitions from holographic random tensor networks

  Romain Vasseur , Andrew C Potter , Yi-Zhuang You , Andreas WW Ludwig

  Physical Review B (13), 134203 (2019)

  We introduce a class of phase transitions separating quantum states with different entanglement features. An example of such an “entanglement phase transition” is provided by the many-body localization transition in disordered quantum systems, as it separates highly entangled thermal states at weak disorder from many-body localized states with low entanglement at strong disorder. In the spirit of random matrix theory, we describe a simple model for such transitions where a physical quantum many-body system lives at the “holographic” boundary of a bulk random tensor network. Using a replica trick approach, we map the calculation of the entanglement properties of the boundary system onto the free energy cost of fluctuating domain walls in a classical statistical mechanics model. This allows us to interpret transitions between volume-law and area-law scaling of entanglement as ordering transitions in this …

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  Emergent Schrödinger equation in an introspective machine learning architecture

  Ce Wang , Hui Zhai , Yi-Zhuang You

  Science Bulletin (17), 1228-1233 (2019)

  Can physical concepts and laws emerge in a neural network as it learns to predict the observation data of physical systems? As a benchmark and a proof-of-principle study of this possibility, here we show an introspective learning architecture that can automatically develop the concept of the quantum wave function and discover the Schrödinger equation from simulated experimental data of the potential-to-density mappings of a quantum particle. This introspective learning architecture contains a machine translator to perform the potential to density mapping, and a knowledge distiller auto-encoder to extract the essential information and its update law from the hidden states of the translator, which turns out to be the quantum wave function and the Schrödinger equation. We envision that our introspective learning architecture can enable machine learning to discover new physics in the future.

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  Emergent symmetry and conserved current at a one-dimensional incarnation of deconfined quantum critical point

  Rui-Zhen Huang , Da-Chuan Lu , Yi-Zhuang You , Zi Yang Meng , Tao Xiang

  Physical Review B (12), 125137 (2019)

  The deconfined quantum critical point (DQCP) was originally proposed as a continuous transition between two spontaneous symmetry breaking phases in 2D spin-1/2 systems. While great efforts have been spent on the DQCP for 2D systems, both theoretically and numerically, ambiguities among the nature of the transition are still not completely clarified. Here we shift the focus to a recently proposed 1D incarnation of DQCP in a spin-1/2 chain. By solving it with the variational matrix product state in the thermodynamic limit, a continuous transition between a valence-bond solid phase and a ferromagnetic phase is discovered. The scaling dimensions of various operators are calculated and compared with those from field theoretical description. At the critical point, two emergent symmetries are revealed, and the associated conserved current operators with exact integer scaling dimensions are determined with …

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  Dynamics of compact quantum electrodynamics at large fermion flavor

  Wei Wang , Da-Chuan Lu , Xiao Yan Xu , Yi-Zhuang You , Zi Yang Meng

  Physical Review B (8), 085123 (2019)

  Thanks to the development in quantum Monte Carlo technique, the compact U(1) lattice gauge theory coupled to fermionic matter at ( )D is now accessible with large-scale numerical simulations, and the ground state phase diagram as a function of fermion flavor ( ) and the strength of gauge fluctuations is mapped out. Here we focus on the large fermion flavor case ( ) to investigate the dynamic properties across the deconfinement-to-confinement phase transition. In the deconfined phase, fermions coupled to the fluctuating gauge field to form U(1) spin liquid with continua in both spin and dimer spectral functions, and in the confined phase fermions are gapped out into valence bond solid phase with translational symmetry breaking and gapped spectra. The dynamical behaviors provide supporting evidence for the existence of the U(1) deconfined phase and could shine light on the nature of the U(1)-to-VBS …

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  Lattice construction of duality with non-Abelian gauge fields in 2+ 1D

  Chao-Ming Jian , Zhen Bi , Yi-Zhuang You

  Physical Review B (7), 075109 (2019)

  The lattice construction of Euclidean path integrals has been a successful approach of deriving 2+1D field theory dualities with a gauge field. In this work, we generalize this lattice construction to dualities with non-Abelian gauge fields. We construct the Euclidean space-time lattice path integral for a theory with strongly interacting vector bosons and Majorana fermions coupled to an gauge field and derive an exact duality between this theory and the theory of a free Majorana fermion on the space-time lattice. We argue that this lattice duality implies the desired infrared duality between the field theory with an vector critical boson coupled to an Chern-Simons gauge theory, and a free massless Majorana fermion in 2+1D. We also generalize the lattice construction of dualities to models with gauge fields.

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  Quantum simulation of the non-fermi-liquid state of Sachdev-Ye-Kitaev model

  Zhihuang Luo , Yi-Zhuang You , Jun Li , Chao-Ming Jian , Dawei Lu , Cenke Xu , Bei Zeng , Raymond Laflamme

  Npj Quantum Information (1), 53 (2019)

  The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here, we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our …

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  Role of Noether’s theorem at the deconfined quantum critical point

  Nvsen Ma , Yi-Zhuang You , Zi Yang Meng

  Physical Review Letters (17), 175701 (2019)

  Noether’s theorem is one of the fundamental laws of physics, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s theorem at the deconfined quantum critical point (DQCP), which is a quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP, which, if true, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectra, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current, as signified by the vanishing anomalous dimension of the current operator, and hence provide supporting evidence for the emergent symmetry at the DQCP. Our study demonstrates an elegant yet practical approach to detect emergent …

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  Superconductivity from valley fluctuations and approximate SO (4) symmetry in a weak coupling theory of twisted bilayer graphene

  Yi-Zhuang You , Ashvin Vishwanath

  Npj Quantum Materials (1), 16 (2019)

  The recent discovery of the Mott insulating and superconducting phases in twisted bilayer graphene has generated tremendous research interest. Here, we develop a weak coupling approach to the superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ( d + i d mixed with p −i p ) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at …

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  Dynamical signature of fractionalization at a deconfined quantum critical point

  Nvsen Ma , Guang-Yu Sun , Yi-Zhuang You , Cenke Xu , Ashvin Vishwanath , Anders W Sandvik , Zi Yang Meng

  Physical Review B (17), 174421 (2018)

  Deconfined quantum critical points govern continuous quantum phase transitions at which fractionalized (deconfined) degrees of freedom emerge. Here we study dynamical signatures of the fractionalized excitations in a quantum magnet (the easy-plane J-Q model) that realize a deconfined quantum critical point with emergent O(4) symmetry. By means of large-scale quantum Monte Carlo simulations and stochastic analytic continuation of imaginary-time correlation functions, we obtain the dynamic spin-structure factors in the and channels. In both channels, we observe broad continua that originate from the deconfined excitations. We further identify several distinct spectral features of the deconfined quantum critical point, including the lower edge of the continuum and its form factor on moving through the Brillouin zone. We provide field-theoretical and lattice model calculations that explain the overall shapes …

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  Candidate theory for the strange metal phase at a finite-energy window

  Xiaochuan Wu , Xiao Chen , Chao-Ming Jian , Yi-Zhuang You , Cenke Xu

  Physical Review B (16), 165117 (2018)

  We propose a lattice model for strongly interacting electrons with the potential to explain the main phenomenology of the strange metal phase in the cuprate high-temperature superconductors. Our model is motivated by the recently developed “tetrahedron” rank-3 tensor model that mimics much of the physics of the better-known Sachdev-Ye-Kitaev (SYK) model. Our electron model has the following advantageous properties: (1) it needs only one orbital per site on the square lattice. (2) It does not require any quenched random interaction. (3) It has local interactions and respects all the symmetries of the system. (4) The soluble limit of this model has a longitudinal dc resistivity that scales linearly with temperature within a finite temperature window. (5) Again, the soluble limit of this model has a fermion pairing instability in the infrared, which can lead to either superconductivity or a “pseudogap” phase. The linear- …

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  Classification of symmetry-protected phases for interacting fermions in two dimensions

  Meng Cheng , Zhen Bi , Yi-Zhuang You , Zheng-Cheng Gu

  Physical Review B (20), 205109 (2018)

  Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry can be completely classified by the group cohomology . Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.

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  Entanglement features of random Hamiltonian dynamics

  Yi-Zhuang You , Yingfei Gu

  ArXiv Preprint arXiv:1803.10425 (2018)

  We introduce the concept of entanglement features of unitary gates, as a collection of exponentiated entanglement entropies over all bipartitions of input and output channels. We obtained the general formula for time-dependent th-Renyi entanglement features for unitary gates generated by random Hamiltonian. In particular, we propose an Ising formulation for the 2nd-Renyi entanglement features of random Hamiltonian dynamics, which admits a holographic tensor network interpretation. As a general description of entanglement properties, we show that the entanglement features can be applied to several dynamical measures of thermalization, including the out-of-time-order correlation and the entanglement growth after a quantum quench. We also analyze the Yoshida-Kitaev probabilistic protocol for random Hamiltonian dynamics.

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  From bosonic topological transition to symmetric fermion mass generation

  Yi-Zhuang You , Yin-Chen He , Ashvin Vishwanath , Cenke Xu

  Physical Review B (12), 125112 (2018)

  A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors ( ). Within a systematic renormalization group analysis, we identify the critical point with the desired emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an quantum chromodynamics-Higgs theory with flavors of fundamental fermions and one fundamental …

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  Machine learning spatial geometry from entanglement features

  Yi-Zhuang You , Zhao Yang , Xiao-Liang Qi

  Physical Review B (4), 045153 (2018)

  Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on a 1D free fermion system and observe the emergence of the hyperbolic geometry ( spatial geometry) as we tune the fermion system …

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  Symmetric fermion mass generation as deconfined quantum criticality

  Yi-Zhuang You , Yin-Chen He , Cenke Xu , Ashvin Vishwanath

  Physical Review X (1), 011026 (2018)

  Massless Dirac fermions arise in a variety of systems from graphene to the surfaces of topological insulators, where generating a mass is typically associated with breaking a symmetry. However, with strong interactions, a symmetric gapped phase can arise for multiples of eight Dirac fermions. A continuous quantum phase transition from the massless Dirac phase to this massive phase, which we term symmetric mass generation, is necessarily beyond the Landau paradigm and is hard to describe even at the conceptual level. Nevertheless, such transition has been consistently observed in several numerical studies recently. Here, we propose a theory for the symmetric mass generation transition which is reminiscent of deconfined criticality and involves emergent non-Abelian gauge fields coupled both to Dirac fermions and to critical Higgs bosons. We motivate the theory using an explicit parton construction …

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  Observing fermion pair instability of the Sachdev-Ye-Kitaev model on a quantum spin simulator

  Zhihuang Luo , Yi-Zhuang You , Jun Li , Chao-Ming Jian , Dawei Lu , Cenke Xu , Bei Zeng , Raymond Laflamme

  ArXiv Preprint arXiv:1712.06458 (2017)

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  Emergent symmetry and tricritical points near the deconfined quantum critical point

  Chao-Ming Jian , Alex Rasmussen , Yi-Zhuang You , Cenke Xu

  ArXiv Preprint arXiv:1708.03050 (2017)

  Recent proposal of the duality between the noncompact QED and the easy-plane noncompact CP (NCCP ) model suggests that the deconfined quantum critical point (dQCP) between the easy-plane antiferromagnet and the VBS order on the square lattice may have an emergent O(4) symmetry, due to the self-duality of the noncompact QED . Recent numerical progresses suggest that this easy-plane dQCP does exist and it has an emergent O(4) symmetry. But for the O(4) symmetry to really emerge at the dQCP, certain O(4) symmetry breaking perturbations need to be irrelevant at the putative O(4) fixed point. It is more convenient to study these symmetry breaking perturbations in the noncompact QED . We demonstrate that a natural large- generalization and a controlled expansion supports the stability of the O(4) fixed point against the symmetry breaking perturbations. We also develop the theory for two tricritical points close to the easy-plane dQCP. One tricritical point is between the dQCP and a {\it self-dual} topological order; the other is the tricritical point that connects the continuous dQCP and a first order N\'{e}el-VBS transition, motivated by recent numerical results.

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  Holographic coherent states from random tensor networks

  Xiao-Liang Qi , Zhao Yang , Yi-Zhuang You

  Journal of High Energy Physics (8), 1-29 (2017)

  Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We setup a framework in which all possible bulk spatial geometries, characterized by weighted adjacient matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded in this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around …

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  Duality between the deconfined quantum-critical point and the bosonic topological transition

  Yan Qi Qin , Yuan-Yao He , Yi-Zhuang You , Zhong-Yi Lu , Arnab Sen , Anders W Sandvik , Cenke Xu , Zi Yang Meng

  Physical Review X (3), 031052 (2017)

  Recently, significant progress has been made in ( )-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities; i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly correlated quantum-matter systems: the one relating the easy-plane noncompact model ( ) and noncompact quantum electrodynamics (QED) with two flavors ( ) of massless two-component Dirac fermions. The easy-plane model is the field theory of the putative deconfined quantum-critical point separating a planar ( ) antiferromagnet and a dimerized (valence-bond solid) ground state, while noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work …

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  Instability of the non-Fermi-liquid state of the Sachdev-Ye-Kitaev model

  Zhen Bi , Chao-Ming Jian , Yi-Zhuang You , Kelly Ann Pawlak , Cenke Xu

  Physical Review B (20), 205105 (2017)

  We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the maximal chaotic non-Fermi-liquid phase described by the ordinary SYK model has marginally relevant or irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the model with a -fermion interaction, similar perturbations can lead to a series of new fixed points with continuously varying exponents.

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  Out-of-time-order correlation in marginal many-body localized systems

  Kevin Slagle , Zhen Bi , Yi-Zhuang You , Cenke Xu

  Physical Review B (16), 165136 (2017)

  We show that the out-of-time-order correlation (OTOC) in many-body localized (MBL) and marginal MBL systems can be efficiently calculated by the spectrum bifurcation renormalization group (SBRG). We find that in marginal MBL systems, the scrambling time follows a stretched exponential scaling with the distance between the operators and : , which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in nonchaotic systems.

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  Bilayer graphene as a platform for bosonic symmetry-protected topological states

  Zhen Bi , Ruixing Zhang , Yi-Zhuang You , Andrea Young , Leon Balents , Chao-Xing Liu , Cenke Xu

  Physical Review Letters (12), 126801 (2017)

  Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of topological insulators, have attracted enormous theoretical interest in the last few years. Although BSPT states have been classified by various approaches, there is so far no successful experimental realization of any BSPT state in two or higher dimensions. In this paper, we propose that a two-dimensional BSPT state with symmetry can be realized in bilayer graphene in a magnetic field. Here the two symmetries represent total spin and total charge conservation, respectively. The Coulomb interaction plays a central role in this proposal—it gaps out all the fermions at the boundary, so that only bosonic charge and spin degrees of freedom are gapless and protected at the edge. Based on the above conclusion, we propose that the bulk quantum phase transition between the BSPT and trivial phase, which can be driven by …

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  Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states

  Yi-Zhuang You , Andreas WW Ludwig , Cenke Xu

  Physical Review B (11), 115150 (2017)

  We consider the Sachdev-Ye-Kitaev (SYK) model as a model for the thermalized zero-dimensional boundary of a many-body localized, fermionic symmetry protected topological (SPT) phase in one spatial dimension. The fermions at the boundary are always fully interacting. We find that the boundary is thermalized and investigate how its boundary anomaly, dictated by the bulk SPT order, is encoded in the quantum chaotic eigenspectrum of the SYK model. We show that depending on the SPT symmetry class, the boundary many-body level statistics cycle in a systematic manner through those of the three different Wigner-Dyson random matrix ensembles with a periodicity in the topological index that matches the interaction-reduced classification of the bulk SPT states. We consider all three symmetry classes BDI, AIII, and CII, whose SPT phases are classified in one spatial dimension by in the absence of …

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  Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

  Yuan-Yao He , Han-Qing Wu , Yi-Zhuang You , Cenke Xu , Zi Yang Meng , Zhong-Yi Lu

  Physical Review B (24), 241111 (2016)

  We study a lattice model of interacting Dirac fermions in dimensions space-time with an SU(4) symmetry. While increasing the interaction strength, this model undergoes a continuous quantum phase transition from a weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progress in the lattice QCD community.

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  Visualizing a bosonic symmetry protected topological phase in an interacting fermion model

  Han-Qing Wu , Yuan-Yao He , Yi-Zhuang You , Tsuneya Yoshida , Norio Kawakami , Cenke Xu , Zi Yang Meng , Zhong-Yi Lu

  Physical Review B (16), 165121 (2016)

  Symmetry protected topological (SPT) phases in free fermion and interacting bosonic systems have been classified, but the physical phenomena of interacting fermionic SPT phases have not been fully explored. Here, employing large-scale quantum Monte Carlo simulation, we investigate the edge physics of a bilayer Kane-Mele-Hubbard model with zigzag ribbon geometry. Our unbiased numerical results show that the fermion edge modes are gapped out by interaction, while the bosonic edge modes remain gapless at the boundary, before the bulk quantum phase transition to a topologically trivial phase. Therefore, finite fermion gaps both in the bulk and on the edge, together with the robust gapless bosonic edge modes, prove that our system becomes an emergent bosonic SPT phase at low energy, which is directly observed in an interacting fermion lattice model.

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  Low-energy spin dynamics of the honeycomb spin liquid beyond the Kitaev limit

  Xue-Yang Song , Yi-Zhuang You , Leon Balents

  Physical Review Letters (3), 037209 (2016)

  We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the , , and points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.

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  Disordered XYZ spin chain simulations using the spectrum bifurcation renormalization group

  Kevin Slagle , Yi-Zhuang You , Cenke Xu

  Physical Review B (1), 014205 (2016)

  We study the disordered XYZ spin chain using the recently developed spectrum bifurcation renormalization group [Y.-Z. You , Phys. Rev. B 93, 104205 (2016)2469-995010.1103/PhysRevB.93.104205] numerical method. With strong disorder, the phase diagram consists of three many-body localized (MBL) spin-glass phases. We argue that, with sufficiently strong disorder, these spin-glass phases are separated by marginally MBL critical lines. We examine the critical lines of this model by measuring the entanglement entropy and Edwards-Anderson spin-glass order parameter, and find that the critical lines are characterized by an effective central charge . Our data also suggest continuously varying critical exponents along the critical lines. We also demonstrate how long-range mutual information [introduced in C.-M. Jian , arXiv:1508.07006] can distinguish these phases.

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  Exotic quantum critical point on the surface of three-dimensional topological insulator

  Zhen Bi , Yi-Zhuang You , Cenke Xu

  Physical Review B (2), 024433 (2016)

  In the last few years a lot of exotic and anomalous topological phases were constructed by proliferating the vortexlike topological defects on the surface of the topological insulator (TI) [Fidkowski , Phys. Rev. X 3, 041016 (2013)10.1103/PhysRevX.3.041016; Chen , Phys. Rev. B 89, 165132 (2014)10.1103/PhysRevB.89.165132; Bonderson , J. Stat. Mech. (2013) P0901610.1088/1742-5468/2013/09/P09016; Wang , Phys. Rev. B 88, 115137 (2013)10.1103/PhysRevB.88.115137; Metlitski , Phys. Rev. B 92, 125111 (2015)10.1103/PhysRevB.92.125111]. In this work, rather than considering topological phases at the boundary, we will study quantum critical points driven by vortexlike topological defects. In general, we will discuss a quantum phase transition described by the following field theory: L=ψ¯γμ(∂μ−iaμ)ψ+|(∂μ−ikaμ)ϕ|2+r|ϕ|2+g|ϕ|4, with tuning parameter , arbitrary integer , Dirac fermion , and complex scalar bosonic field …

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  Geometry defects in bosonic symmetry-protected topological phases

  Yizhi You , Yi-Zhuang You

  Physical Review B (24), 245135 (2016)

  In this paper we focus on the interplay between geometry defects and topological properties in bosonic symmetry-protected topological (SPT) phases. We start from eight copies of 3D time-reversal invariant topological superconductors (TSC) on a crystal lattice. We melt the lattice by condensation of disclinations and therefore restore the rotation symmetry. Such a disclination condensation procedure confines the fermion and afterwards turns the system into a 3D boson topological liquid crystal (TCL). The low energy effective theory of this crystalline-liquid transition contains a topological term inherited from the geometry axion response in TSC. In addition, we investigate the interplay between dislocation and superfluid vortex on the surface of TCL. We demonstrate that the and translation invariant surface state is a double state with intrinsic surface topological order. We also look into the exotic behavior of dislocation in the 2D …

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  Stripe melting and a transition between weak and strong symmetry protected topological phases

  Yizhi You , Yi-Zhuang You

  Physical Review B (19), 195141 (2016)

  For a gapped disordered many-body system with both internal and translation symmetry, one can define the corresponding weak and strong symmetry protected topological (SPT) phases. A strong SPT phase is protected by the internal symmetry only while a weak SPT phase, fabricated by alignment of a strong SPT state in a lower dimension, requires additional discrete translation symmetry protection. In this paper, we construct a phase transition between weak and strong SPT phase in a strongly interacting boson system. The starting point of our construction is the superconducting Dirac fermions with pair density wave (PDW) order in . We first demonstrate that the nodal line of the PDW contains a boson SPT phase. We further show that melting the PDW stripe and condensing the nodal line provoke the transition from weak to strong SPT phase in . The phase transition theory contains an O(4) nonlinear …

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  Bona fide interaction-driven topological phase transition in correlated symmetry-protected topological states

  Yuan-Yao He , Han-Qing Wu , Yi-Zhuang You , Cenke Xu , Zi Yang Meng , Zhong-Yi Lu

  Physical Review B (11), 115150 (2016)

  It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this …

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  Quantum phase transitions between bosonic symmetry-protected topological states without sign problem: Nonlinear sigma model with a topological term

  Yi-Zhuang You , Zhen Bi , Dan Mao , Cenke Xu

  Physical Review B (12), 125101 (2016)

  We propose a series of simple two-dimensional (2D) lattice interacting fermion models that we demonstrate at low energy describe bosonic symmetry-protected topological (SPT) states and quantum phase transitions between them. This is because due to interaction, the fermions are gapped both at the boundary of the SPT states and at the bulk quantum phase transition, thus these models at low energy can be described completely by bosonic degrees of freedom. We show that the bulk of these models is described by a ) principal chiral model with a topological term, whose boundary is described by a ) principal chiral model with a Wess-Zumino-Witten term at level 1. The quantum phase transition between SPT states in the bulk is tuned by a particular interaction term, which corresponds to tuning in the field theory, and the phase transition occurs at . The simplest version of these models with is equivalent to …

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  Entanglement holographic mapping of many-body localized system by spectrum bifurcation renormalization group

  Yi-Zhuang You , Xiao-Liang Qi , Cenke Xu

  Physical Review B (10), 104205 (2016)

  We introduce the spectrum bifurcation renormalization group (SBRG) as an improved application of the excited-state real-space renormalization group (RSRG-X) for a class of qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to many interacting spin and fermion models in the full MBL phase. As a Hilbert-space preserving RG, SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.

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  Stable gapless bose liquid phases without any symmetry

  Alex Rasmussen , Yi-Zhuang You , Cenke Xu

  ArXiv Preprint arXiv:1601.08235 (2016)

  It is well-known that a stable algebraic spin liquid state (or equivalently an algebraic Bose liquid (ABL) state) with emergent gapless photon excitations can exist in quantum spin ice systems, or in a quantum dimer model on a bipartite lattice. This photon phase is stable against any weak perturbation without assuming any symmetry. Further works concluded that certain lattice models give rise to more exotic stable algebraic Bose liquid phases with graviton-like excitations. In this paper we will show how these algebraic Bose liquid states can be generalized to stable phases with even more exotic types of gapless excitations and then argue that these new phases are stable against weak perturbations. We also explicitly show that these theories have an (algebraic) topological ground state degeneracy on a torus, and construct the corresponding topological invariants.

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  Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator

  Cenke Xu , Yi-Zhuang You

  Physical Review B (22), 220416 (2015)

  Inspired by recent developments in constructing novel Dirac liquid boundary states of a three-dimensional (3D) topological insulator, we propose one possible two-dimensional boundary state of a 3D bosonic symmetry protected topological state with symmetry. This boundary theory is described by a -dimensional quantum electrodynamics with two flavors of Dirac fermions coupled with a noncompact U(1) gauge field, L=∑j=12ψ¯jγμ(∂μ−iaμ)ψj−iAμsψi¯γμτijzψj+i2πεμνρaμ∂νAρe, where is the internal noncompact U(1) gauge field, and and are two external gauge fields that couple to and global symmetries, respectively. We demonstrate that this theory has a “self-dual” structure, which is a fermionic analog of the self-duality of the noncompact theory with easy plane anisotropy. Under the self-duality, the boundary action takes exactly the same form except for an …

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  Quantum Monte Carlo study of strange correlator in interacting topological insulators

  Han-Qing Wu , Yuan-Yao He , Yi-Zhuang You , Cenke Xu , Zi Yang Meng , Zhong-Yi Lu

  Physical Review B (16), 165123 (2015)

  Distinguishing the nontrivial symmetry-protected topological (SPT) phase from the trivial insulator phase in the presence of electron-electron interaction is an urgent question to the study of topological insulators, due to the fact that most of the topological indices defined for free electron systems are very likely unsuitable for interacting cases. In this work, we demonstrate that the strange correlator is a sensitive diagnosis to detect SPT states in interacting systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we investigate the interaction-driven quantum phase transition in the Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at weak interaction to an antiferromagnetic Mott insulator at strong interaction can be readily detected by the momentum space behavior of the strange correlator in single-particle, spin, and pairing sectors. The interaction effects on the symmetry …

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  Topological orders with global gauge anomalies

  Yi-Zhuang You , Cenke Xu

  Physical Review B (5), 054410 (2015)

  By definition, the physics of the -dimensional (dim) boundary of a -dim symmetry protected topological (SPT) state cannot be realized as itself on a -dim lattice. If the symmetry of the system is unitary, then a formal way to determine whether a -dim theory must be a boundary or not, is to couple this theory to a gauge field (or to “gauge” its symmetry), and check if there is a gauge anomaly. In this paper we discuss the following question: Can the boundary of a SPT state be driven into a fully gapped topological order which preserves all the symmetries? We argue (conjecture) that if the gauge anomaly of the boundary is “perturbative,” then the boundary must remain gapless; while if the boundary only has global gauge anomaly but no perturbative anomaly, then it is possible to gap out the boundary by driving it into a topological state, when . We will demonstrate this conjecture with two examples: (1) the spin-1/2 chiral fermion with the …

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  Bridging fermionic and bosonic short range entangled states

  Yi-Zhuang You , Zhen Bi , Alex Rasmussen , Meng Cheng , Cenke Xu

  New Journal of Physics, 075010 (2015)

  In this paper we construct bosonic short range entangled (SRE) states in all spatial dimensions by coupling a

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  Many-body localization of symmetry protected topological states

  Kevin Slagle , Zhen Bi , Yi-Zhuang You , Cenke Xu

  ArXiv Preprint arXiv:1505.05147 (2015)

  We address the following question: Which kinds of symmetry protected topological (SPT) Hamiltonians can be many-body localized? That is, which Hamiltonians with an SPT ground state have finite energy density excited states which are all localized by disorder? Based on the observation that a finite energy density state, if localized, can be viewed as the ground state of a local Hamiltonian, we propose a simple (though possibly incomplete) rule for many-body localization of SPT Hamiltonians: If the ground state and top state (highest energy state) belong to the same SPT phase, then it is possible to localize all the finite energy density states; If the ground and top state belong to different SPT phases, then most likely there are some finite energy density states which can not be fully localized. We will give concrete examples of both scenarios. In some of these examples, we argue that interaction can actually "assist" localization of finite energy density states, which is counter-intuitive to what is usually expected.

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  Interacting topological insulator and emergent grand unified theory

  Yi-Zhuang You , Cenke Xu

  Physical Review B (12), 125147 (2015)

  Motivated by the Pati-Salam grand unified theory [J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974)0556-282110.1103/PhysRevD.10.275], we study topological insulators with symmetry, whose boundary has 16 flavors of left-chiral fermions, which form representations and . The key result we obtain is that, without any interaction, this topological insulator has a classification, namely, any quadratic fermion mass operator at the boundary is prohibited by the symmetries listed above; while under interaction, this system becomes trivial, namely, its boundary can be gapped out by a properly designed short-range interaction without generating nonzero vacuum expectation value of any fermion bilinear mass, or in other words, its boundary can be driven into a “strongly-coupled symmetric gapped (SCSG) phase.” Based on this observation, we propose that after …

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  Exotic quantum phase transitions of strongly interacting topological insulators

  Kevin Slagle , Yi-Zhuang You , Cenke Xu

  Physical Review B (11), 115121 (2015)

  Using determinant quantum Monte Carlo simulations, we demonstrate that an extended Hubbard model on a bilayer honeycomb lattice has two novel quantum phase transitions. The first is a quantum phase transition between the weakly interacting gapless Dirac fermion phase and a strongly interacting fully gapped and symmetric trivial phase, which cannot be described by the standard Gross-Neveu model. The second is a quantum critical point between a quantum spin Hall insulator with spin conservation and the previously mentioned strongly interacting fully gapped phase. At the latter quantum critical point the single-particle excitations remain gapped, while spin and charge gaps both close. We argue that the first quantum phase transition is related to the classification of the topological superconductor phase with interactions, while the second quantum phase transition is a topological phase transition …

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  Measuring modular matrices by shearing lattices

  Yi-Zhuang You , Meng Cheng

  ArXiv Preprint arXiv:1502.03192 (2015)

  A topologically ordered phase on a torus possesses degenerate ground states that transform nontrivially under the modular transformations of the torus, generated by Dehn twists. Representation of modular transformations on the ground states (modular matrices) characterizes the topological order. We show that the modular matrices can be numerically measured as the non-Abelian Berry phase of adiabatic deformations of the lattice model placed on a torus. We apply this method to the example of a gauged superconductor, and show that the result is consistent with the topological quantum field theory descriptions.

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  Bosonic short-range entangled states beyond group cohomology classification

  Cenke Xu , Yi-Zhuang You

  Physical Review B (5), 054406 (2015)

  We explore and construct a class of bosonic short-range entangled (BSRE) states in all spatial dimensions, which are higher dimensional generalizations of the well-known Kitaev's state in [Ann. Phys. (N.Y.) 321, 2 (2006)APNYA60003-491610.1016/j.aop.2005.10.005; http://online.kitp.ucsb.edu/online/topomat11/kitaev]. These BSRE states share the following properties: (1) their bulk is fully gapped and nondegenerate; (2) their boundary is described by a “self-dual” rank- antisymmetric tensor gauge field, and it is guaranteed to be gapless without assuming any symmetry; (3) their boundary has intrinsic gravitational anomaly once coupled to the gravitational field; (4) their bulk is described by an effective Chern-Simons field theory with rank- antisymmetric tensor fields, whose matrix is identical to that of the state in ; (5) the existence of these BSRE states leads to various bosonic symmetry protected …

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  Symmetry-protected topological states of interacting fermions and bosons

  Yi-Zhuang You , Cenke Xu

  Physical Review B (24), 245120 (2014)

  We study the classification for a large class of interacting fermionic and bosonic symmetry-protected topological (SPT) states, focusing on the cases where interaction reduces the classification of free-fermion SPT states. We define a SPT state as whether it is separated from the trivial state through a bulk phase transition, which is a general definition applicable to SPT states with or without spatial symmetries. We show that in all dimensions short-range interactions can reduce the classification of free-fermion SPT states, and we demonstrate these results by making a connection between the fermionic and bosonic SPT states. We first demonstrate that our formalism gives the correct classification for several known SPT states, with or without interaction, and then we generalize our method to SPT states that involve the spatial inversion symmetry.

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  Coexisting itinerant and localized electrons

  Yi-Zhuang You , Zheng-Yu Weng

  Iron-Based Superconductivity, 377-408, 2014, 377-408 (2014)

  The surprising discovery of high- T c superconductivity in iron-based compounds has prompted an intensive investigation on the role of interaction and magnetism in these materials. Based on the general features of multi-bands and intermediate coupling strengths, a phenomenological theory based on the coexistence of the itinerant electrons and local moments has been proposed to describe the low-energy physics in iron-based superconductors. It provides a unified minimal framework to understand magnetic, superconducting, and normal phases in these materials, which is subject to further microscopic justification and experimental verification.

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  Anyon and loop braiding statistics in field theories with a topological Θ term

  Zhen Bi , Yi-Zhuang You , Cenke Xu

  Physical Review B (8), 081110 (2014)

  We demonstrate that the anyon statistics and three-loop statistics of various and topological phases can be derived using semiclassical nonlinear sigma model field theories with a topological term. In our formalism, the braiding statistics has a natural geometric meaning: The braiding process of anyons or loops leads to a nontrivial field configuration in the space-time, which will contribute a braiding phase factor due to the term.

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  Topological number and fermion Green's function for strongly interacting topological superconductors

  Yi-Zhuang You , Zhong Wang , Jeremy Oon , Cenke Xu

  Physical Review B (6), 060502 (2014)

  It has been understood that short range interactions can reduce the classification of topological superconductors in all dimensions. In this Rapid Communication we demonstrate by explicit calculations that when the topological phase transition between two distinct phases in the noninteracting limit is gapped out by interaction, the bulk fermion Green's function at the “transition” approaches zero as at certain momentum in the Brillouin zone.

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  Observation of Momentum-Confined In-Gap Impurity State in Ba0.6K0.4Fe2As2: Evidence for Antiphase s± Pairing

  Peng Zhang , Pierre Richard , Tian Qian , Xun Shi , Jun Ma , L-K Zeng , X-P Wang , Emile Rienks , C-L Zhang , Pengcheng Dai , Y-Z You , Z-Y Weng , X-X Wu , JP Hu , Hong Ding

  Physical Review X (3), 031001 (2014)

  We report the observation by angle-resolved photoemission spectroscopy of an impurity state located inside the superconducting gap of and vanishing above the superconducting critical temperature, for which the spectral weight is confined in momentum space near the Fermi wave-vector positions. We demonstrate, supported by theoretical simulations, that this in-gap state originates from weak scattering between bands with opposite sign of the superconducting-gap phase. This weak scattering, likely due to off-plane nonmagnetic (Ba, K) disorder, occurs mostly among neighboring Fermi surfaces, suggesting that the superconducting-gap phase changes sign within holelike (and electronlike) bands. Our results impose severe restrictions on the models promoted to explain high-temperature superconductivity in these materials.

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  Wave function and strange correlator of short-range entangled states

  Yi-Zhuang You , Zhen Bi , Alex Rasmussen , Kevin Slagle , Cenke Xu

  Physical Review Letters (24), 247202 (2014)

  We demonstrate the following conclusion: If is a one-dimensional (1D) or two-dimensional (2D) nontrivial short-range entangled state and is a trivial disordered state defined on the same Hilbert space, then the following quantity (so-called “strange correlator”) either saturates to a constant or decays as a power law in the limit , even though both and are quantum disordered states with short-range correlation; is some local operator in the Hilbert space. This result is obtained based on both field theory analysis and an explicit computation of for four different examples: 1D Haldane phase of spin-1 chain, 2D quantum spin Hall insulator with a strong Rashba spin-orbit coupling, 2D spin-2 Affleck-Kennedy-Lieb-Tasaki state on the square lattice, and the 2D bosonic symmetry-protected topological phase with symmetry. This result can be used as a …

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  Interacting Topological Superconductors and possible Origin of 16n Chiral Fermions in the Standard Model

  Yi-Zhuang You , Yoni BenTov , Cenke Xu

  ArXiv Preprint arXiv:1402.4151 (2014)

  Motivated by the observation that the Standard Model of particle physics (plus a right-handed neutrino) has precisely 16 Weyl fermions per generation, we search for -dimensional chiral fermionic theories and chiral gauge theories that can be regularized on a 3 dimensional spatial lattice when and only when the number of flavors is an integral multiple of 16. All these results are based on the observation that local interactions reduce the classification of certain -dimensional topological superconductors from to , which means that one of their -dimensional boundaries can be gapped out by interactions without breaking any symmetry when and only when the number of boundary chiral fermions is an integral multiple of .

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  Two-fluid description for iron-based superconductors

  Yi-Zhuang You , Zheng-Yu Weng

  New Journal of Physics (2), 023001 (2014)

  We present a two-fluid description for iron-based superconductors, which contains an itinerant electron Fermi-liquid and a local moment spin-liquid, coupled together via an effective Hund's rule interaction. We examine the low-energy collective behavior of such a system. We find that an electron–spinon composite mode emerges in the intermediate coupling regime, which may account for the hump-dip behavior observed in the recent scanning tunneling spectroscopy experiments. The superconductivity and spin-density-wave phases are consistently described within the same framework. Possible experimental tests are also proposed.

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  Modular transformations and topological orders in two dimensions

  Fangzhou Liu , Zhenghan Wang , Yi-Zhuang You , Xiao-Gang Wen

  ArXiv Preprint arXiv:1303.0829 (2013)

  The string-net approach by Levin and Wen and the local unitary transformation approach by Chen, Gu and Wen provided ways to systematically label non-chiral topological orders in 2D. In those approaches, different topologically ordered many-body wave functions were characterized by different fixed-point tensors. Though extremely powerful, the resulting fixed-point tensors were mathematical abstractions and thus lacked a physical interpretation. As a result it was hard to judge if two different fixed-point tensors described the same quantum phase or not. We want to improve that approach by giving a more physical description of the topological orders. We find that the non-Abelian Berry's phases, - and -matrices, of the topological protected degenerate ground states on a torus give rise to a more physical description of topological orders. Using the Verlinde conjecture, we can even choose the canonical basis for the - and -matrices. It is conjectured that the and -matrices form a complete and one-to-one characterization of non-chiral topological orders and can replace the fixed-point tensor description to give us a more physical label for topological orders. As a result, all the topological properties can be obtained from the - and -matrices, such as number of quasiparticle types (from the dimension of or ), the quasiparticle statistics (from the diagonal elements of ), the quantum dimensions of quasiparticles (from the first row of ), \etc.

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  Synthetic non-Abelian statistics by Abelian anyon condensation

  Yi-Zhuang You , Chao-Ming Jian , Xiao-Gang Wen

  Physical Review B (4), 045106 (2013)

  Topological degeneracy is the degeneracy of the ground states in a many-body system in the large-system-size limit. Topological degeneracy cannot be lifted by any local perturbation of the Hamiltonian. The topological degeneracies on closed manifolds have been used to discover/define topological order in many-body systems, which contain excitations with fractional statistics. In this paper, we study a new type of topological degeneracy induced by condensing anyons along a line in two-dimensional topological ordered states. Such topological degeneracy can be viewed as carried by each end of the line defect, which is a generalization of Majorana zero modes. The topological degeneracy can be used as a quantum memory. The ends of line defects carry projective non-Abelian statistics even though they are produced by the condensation of Abelian anyons, and braiding them allows us to perform fault tolerant …

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  Superfluidity of bosons in kagome lattices with frustration

  Yi-Zhuang You , Zhu Chen , Xiao-Qi Sun , Hui Zhai

  Physical Review Letters (26), 265302 (2012)

  In this Letter we consider spinless bosons in a kagome lattice with nearest-neighbor hopping and on-site interaction, and the sign of hopping is inverted by insetting a flux in each triangle of the kagome lattice so that the lowest single particle band is perfectly flat. We show that in the high-density limit, despite the infinite degeneracy of the single particle ground states, interaction will select out the Bloch state at the point of the Brillouin zone for boson condensation at the lowest temperature. As the temperature increases, the single-boson superfluid order can be easily destroyed, while an exotic triple-boson paired superfluid order will remain. We establish that this trion superfluid exists in a broad temperature regime until the temperature is increased to the same order of hopping and then the system turns into normal phases. Finally, we show that time-of-flight measurement of the momentum distribution and its …

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  Projective non-Abelian statistics of dislocation defects in a ZN rotor model

  Yi-Zhuang You , Xiao-Gang Wen

  Physical Review B (16), 161107 (2012)

  Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations . Here we construct a rotor model that realizes a self-dual Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension . Exchanging dislocations can produce topologically protected projective non-Abelian geometric phases. Therefore, we discover a kind of (projective) non-Abelian anyon that appears as the dislocations in an Abelian rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes.

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  Doping a spin-orbit Mott insulator: Topological superconductivity from the Kitaev-Heisenberg model and possible application to (Na2/Li2)IrO3

  Yi-Zhuang You , Itamar Kimchi , Ashvin Vishwanath

  Physical Review B (8), 085145 (2012)

  We study the effects of doping a Mott insulator on the honeycomb lattice where spins interact via direction-dependent Kitaev couplings , and weak antiferromagnetic Heisenberg couplings . This model is known to have a spin-liquid ground state and may potentially be realized in correlated insulators with strong spin -orbit coupling. The effect of hole doping is studied within a - - model, treated using the SU(2) slave boson formalism, which correctly captures the parent spin liquid. We find superconductor ground states with spin triplet pairing that spontaneously break time-reversal symmetry. Interestingly, the pairing is qualitatively different at low and high dopings, and undergoes a first-order transition with doping. At high dopings, it is smoothly connected to a paired state of electrons propagating with the underlying free particle dispersion. However, at low dopings the dispersion is strongly influenced by the magnetic …

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  Evolution from Unconventional Spin Density Wave to Superconductivity and a Pseudogaplike Phase in NaFe1-xCoxAs

  Xiaodong Zhou , Peng Cai , Aifeng Wang , Wei Ruan , Cun Ye , Xianhui Chen , Yizhuang You , Zheng-Yu Weng , Yayu Wang

  Physical Review Letters (3), 037002 (2012)

  We report the doping, temperature, and spatial evolutions of the electronic structure of studied by scanning tunneling microscopy. In the parent state we directly observe the spin density wave gap, which exhibits unconventional features that are incompatible with simple Fermi surface nesting. The optimally doped sample has a single superconducting gap, but in the overdoped regime a novel pseudogaplike feature emerges. The pseudogaplike phase coexists with superconductivity in the ground state, persists well into the normal state, and shows strong spatial variations. The characteristics of the three distinct electronic states revealed here shed important new lights on the microscopic models for the iron-based superconductors.

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  Kitaev-Heisenberg-J2-J3 model for the iridates A2IrO3

  Itamar Kimchi , Yi-Zhuang You

  Physical Review B (18), 180407 (2011)

  A Kitaev-Heisenberg- - model is proposed to describe the Mott-insulating layered iridates IrO ( , Li). The model is a combination of the Kitaev honeycomb model and the Heisenberg model with all three nearest-neighbor couplings , , and . A rich phase diagram is obtained at the classical level, including the experimentally suggested zigzag ordered phase; as well as the stripy phase, which extends from the Kitaev-Heisenberg limit to the - - one. Combining the experimentally observed spin order with the optimal fitting to the uniform magnetic susceptibility data gives an estimate of possible parameter values, which in turn reaffirms the necessity of including both the Kitaev and farther neighbor couplings.

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  Phase Diagram and a Possible Unified Description of Intercalated Iron Selenide Superconductors

  Yi-Zhuang You , Fan Yang , Su-Peng Kou , Zheng-Yu Weng

  Physical Review Letters (16), 167001 (2011)

  We propose a theoretical description of the phase diagram and physical properties in -type ( , Tl) compounds based on a coexistent local moment and itinerant electron picture. Using neutron scattering and angle-resolved photoemission spectroscopy measurements to fix the general structure of the local moment and itinerant Fermi pockets, we find a superconducting phase with -wave pairing at the pockets and an incipient sign-change wave near the point, which is adjacent to the insulating phases. The uniform susceptibility and resistivity are found to be consistent with the experiment. The main distinction with iron pnictide superconductors is also discussed.

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  Magnetic and superconducting instabilities in a hybrid model of itinerant/localized electrons for iron pnictides

  Yi-Zhuang You , Fan Yang , Su-Peng Kou , Zheng-Yu Weng

  Physical Review B (5), 054527 (2011)

  We study a unified mechanism for spin-density-wave (SDW) and superconductivity in a minimal model in which itinerant electrons and local moments coexist as previously proposed for the iron pnictides [Kou, Li, Weng, EPL 88, 17010 (2009)EULEEJ0295-507510.1209/0295-5075/88/17010]. The phase diagram obtained at the mean-field level is in qualitative agreement with the experiment, which shows how the magnetic and superconducting (SC) instabilities are driven by the critical coupling between the itinerant/localized electrons. The spin and charge response functions at the random-phase-approximation level further characterize the dynamical evolution of the system. In particular, the dynamic spin susceptibility displays a Goldstone mode in the SDW phase, which evolves into a gapped resonance-like mode in the SC phase. The latter persists all the way into the normal state above where a strong …

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  Spin excitations of the block-antiferromagnetic state in K0.8Fe1.6Se2

  Yi-Zhuang You , Hong Yao , Dung-Hai Lee

  Physical Review B (2), 020406 (2011)

  We study the spin excitations of the block-antiferromagnetic state in K Fe Se . Due to the nature of block antiferromagnetism, we expect spin-wave excitations to possess both Goldstone modes and optical branches. We use a simple model Hamiltonian to demonstrate this idea and compute the dispersion and the dynamic spin structure factor using explicit parameters. Our prediction can be directly tested by inelastic neutron-scattering experiments.

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  One-dimensional w-component fermions and bosons with repulsive delta function interaction

  CN Yang , Yi-Zhuang You

  Chinese Physics Letters (2), 020503 (2011)

  We prove in theorems 2 and 3 that for 1D Bosons with repulsive delta function interaction with any number of components and any Young tableau, the energy per particle as N→∞ is the same as for spinless Bosons.

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  Ground State Energy of One-Dimensional δ-Function Interacting Bose and Fermi Gas

  Yi-Zhuang You

  Chin. Phys. Lett. (8), 080305-080305 (2010)

  The ground state energy curves of one-dimensional δ-function interacting bose and fermi gas are fitted with simple algebraic approximations according to their asymptotic behaviors.

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  A new method to demonstrate frustrated total internal reflection in the visible band

  Yizhuang You , Xiaohan Wang , Sihui Wang , Yonghua Pan , Jin Zhou

  American Journal of Physics (3), 224-228 (2008)

  Total reflection occurs when light travels from a medium with refractive index n to an optically less dense medium with refractive index n 0 at an incident angle equal to or greater than the critical angle θ c= arcsin (n 0∕ n)⁠. Besides being totally reflected, the incoming light penetrates into the less dense medium as an evanescent wave and travels for some distance parallel to the interface before being scattered back to the denser medium. If a third medium of refractive index n (that is, made of the same material as the first medium) is placed at a small distance d (of the same order of magnitude as the light wavelength) to the first medium, the incident light can travel partly through the middle medium into the third medium, and the reflected light in the first medium is weakened. This intriguing phenomenon is termed frustrated total internal reflection. A detailed review of theoretical and experimental studies on frustrated …

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  音叉振动阻尼系数的测定与研究

  尤亦庄 , 王晓翰 , 王喆 , 龚国斌 , 潘永华

  大学物理 (5), 58-58 (2007)

  利用计算机的声卡采集音叉振动信号, 研究了振动衰减过程中阻尼系数的大小, 得出了阻尼系数不是常数, 而是与音叉振幅成线性关系的初步结论, 并用共振态下策动力振幅对音叉振幅的关系验证了这一结论. 根据阻尼系数与振幅的关系解释了两种传统方法测量结果差别很大的原因.

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  相位差法测受迫振动的阻尼系数

  王晓翰 , 王喆 , 尤亦庄 , 龚国斌 , 潘永华

  物理实验 (7), 29-30 (2007)

  利用音叉在受迫阻尼振动中速度与驱动力之间的相位差测定了阻尼系数.该方法在系统的稳定状态下读数,克服了通常所用的振幅衰减方法中的不稳定性,可降低人为因素给测量带来的误差.

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Selected Talk Slides

Emergent Classicality from Information Bottleneck

Classical Shadow Tomography

Symmetric Mass Generation

Renormalization Group Flow and Generative Modeling

Machine Learning Physics

Deconfined Quantum Critical Point

Twisted Bilayer Graphene

Spectrum Bifurcation Renormalization Group