Physics, at its essence, strives to decipher the nature across scales, ranging from minuscule atoms to colossal galaxies. To navigate through these vastly divergent scales, physicists employ a theoretical tool known as the renormalization group. This tool connects the behavior of systems across different scales by scale transformations. Traditionally, physicists have crafted these scale transformations manually, relying heavily on intuition and expertise. However, this manual process is laborious and bounded by the limits of human imagination.

Our novel MLRG algorithm (arXiv:2306.11054) transcends these limitations by architecting a multi-tiered, multi-agent artificial intelligence (AI) system that learns optimal scale transformations autonomously. To grasp the essence of our MLRG algorithm, envision a physics classroom with three characters — a meticulous professor, a forgetful student, and a wise principal, all embarking on a journey to explore statistical physics systems of spins on a large lattice.

The meticulous professor embodies the “teacher” model — a generative model residing on a fine-grained lattice, possessing profound knowledge of microscopic physics. This professor likes to generate a large amount of detailed training examples for the student, by randomly sampling fine-grained spin configurations.

On the other hand, the forgetful student represents the “student” model — another generative model, albeit on a coarse-grained sub-lattice. This student is not very careful in studying, often overlooking details and retaining only rough impressions. It endeavors to distill the coarse-grained features of spin configurations to match the intricate examples provided by the teacher, employing simpler models with lesser degrees of freedom. The discrepancy between the teacher and student models furnishes a learning cue to the student, nudging it towards discerning the optimal coarse-graining rule to extract the most essential features.

This teacher-student learning dynamic exploits the power of generative models in unsupervised representation learning, enabling a data-driven automated design of the Renormalization Group (RG) transformation. Generation by generation, as students grow into teachers and pass down lossy knowledge to new students, the spin configurations in their minds undergo progressive coarsening, realizing the RG flow within the physical system.

The wise principal serves as the “moderator” model — a higher-level predictive model. It closely observes how the teacher-student interactions unfold across many lessons. From these observations, the principal unravels how the teacher model parameters influence the student model parameters, effectively learning the flow of model parameters akin to the RG flow in parameter space. As the “moderator” model acquires insight into the RG flow, it can recommend new parameter points, serving as new learning materials, to the “teacher” and “student” models for further training.

In this way, the MLRG algorithm can automatically explore a large parameter space of possible physical models, and discover the key patterns governing how the model’s behavior changes with scale — the very essence of renormalization group principles. The method becomes more accurate as the neural networks grow in complexity. This creative multi-agent approach allows AI to learn physics in a self-supervised manner!

Remarkably, the AI system develops an abstract understanding of concepts like RG monotone, phase transitions, and critical exponents without needing explicit physics built-in. We showcased this by deploying MLRG to scrutinize lattice spin models with Ising symmetry. With ample neural network capacity, the algorithm accurately predicted the critical temperature and other properties pertinent to the Ising phase transition.

This self-learning ability could greatly accelerate physics research. The MLRG method can efficiently explore vast parameter spaces, locate phase transitions, and extract universal properties. It may even uncover unexpected connections between different physical models. More broadly, designing AI with the capacity for abstraction and self-supervised learning can enable scientific insights beyond what human minds can conceive.

The race is on to develop more powerful AI algorithms that can peer into nature’s secrets. MLRG offers a glimpse into a future where AI and physics research complement each other — with machines learning to actively participate in the grand quest to understand our universe.

(Written by Anthropic Claude2)

Related GitHub code repo: EverettYou/MLRG

]]>In our recent work (arXiv:2212.13364), we studied SMG transitions in a theoretical model consisting of a bilayer honeycomb lattice. This model is inspired by real materials like twisted bilayer graphene. Using advanced numerical techniques called variational Monte Carlo simulations, we demonstrated that the Dirac fermions in this model can undergo a direct transition from a massless semimetal state into a gapped, symmetric insulator state, as the strength of interlayer interaction is increased.

Our key finding is that the critical point between the semimetal and insulator appears to be described by an exotic theory called a fermionic deconfined quantum critical point (fDQCP). This theory predicts that right at the transition, the electrons fractionalize into two types of emergent quantum particles - bosonic spinons and fermionic chargons. Our numerical estimate of the fermion scaling dimension at the critical point matches the fDQCP prediction, providing evidence that the fermion indeed splits apart temporarily at this transition.

Importantly, this unconventional metal-insulator transition does not admit a simple mean-field description and goes beyond the textbook Landau paradigm of phase transitions. Unraveling the mechanism of SMG transitions enhances our knowledge of quantum criticality in strongly correlated systems.

Mass generation by fermion fractionalization may also shed light on other puzzles like high temperature superconductivity (arXiv:2308.11195). Furthermore, identifying candidate materials that exhibit SMG can guide the way towards realizing exotic particles like spinons and chargons in real quantum materials. We hope our work stimulates further studies, both theoretical and experimental, on this unusual route to creating excitation gaps in quantum matter.

(Written by Anthropic Claude2)

]]>High-temperature superconductors have the potential to revolutionize a myriad of technologies, from more efficient electrical grids to faster computers and cutting-edge medical devices. While this phenomenon had been previously observed in other transition metal compounds like cuprates and iron-pnictides, the addition of nickelate compounds to this exclusive club is particularly exciting. The discovery of superconductivity in the chemical compound \(\text{La}_3\text{Ni}_2\text{O}_7\) (see Figure 1) has generated a wave of excitement in the world of condensed matter physics, adding a new dimension to the already significant field of high-temperature superconductors. This nickelate superconductor manifests fascinating properties in an orthorhombic phase under high pressure, reaching a transition temperature (Tc) as high as 80 K.

This nickelate superconductor is special not just for being a new family in the high-temperature superconductor realm but also for its unique properties. To appreciate the peculiarity of nickelates, it’s crucial to understand a bit about their well-studied cousins, the cuprates. Cuprates are single-layer materials that exhibit fascinating phenomena like the Lieb-Schultz-Mattis (LSM) anomaly in their Mott insulating phase. In layman’s terms, the LSM anomaly implies that the Mott insulating phase of cuprates can’t be “ordinary”: it has to break certain symmetries or manifest complex topological states. Nickelates are different. They are bilayer materials, and this two-layer structure cancels out the LSM anomaly, allowing for a more straightforward, or “trivial,” Mott state, which we called a Symmetric Mass Generation (SMG) insulator (arXiv:2307.12223). This makes nickelates a playground for phenomena less convoluted than those in cuprates, offering new opportunities for both theoretical and experimental research.

Two remarkable features of nickelate superconductors are particularly baffling. First, their critical temperature — the temperature below which they become superconductors — actually decreases with pressure. This is a head-scratcher because it contradicts what we commonly observe: that higher pressure should lead to higher critical temperatures, since more pressure usually means greater lattice vibrations or stronger magnetic fluctuations — both factors that typically boost superconductivity. Second, nickelates exhibit something known as “strange metal behavior” at temperatures above their superconducting phase, indicative of strong quantum fluctuations and proximity to some mysterious quantum states that scientists are keen to understand.

In our recent paper (arXiv:2308.11195), we delved into the enigmatic properties of \(\text{La}_3\text{Ni}_2\text{O}_7\) by developing a comprehensive bilayer square lattice model, which incorporates interlayer Heisenberg interaction to unravel the complex behaviors observed in this nickelate compound. Employing rigorous calculations and utilizing both weak and strong coupling perspectives through BCS and BEC mean-field theories, we elucidated a range of mechanisms by which high-temperature superconductivity could arise in this compound. Our work not only maps out a detailed phase diagram (see Figure 2) based on the electron interaction strength and filling fraction, but also provides invaluable insights into why Tc decreases with pressure and what drives the strange metal behavior in nickelates. This research serves as a roadmap for future experiments and elevates our understanding of high-temperature superconductivity, a phenomenon that has the potential to transform our technological landscape.

Our findings indicate that both nickel \(3d_{z^2}\) and \(3d_{x^2-y^2}\) orbitals can exhibit superconductivity in \(\text{La}_3\text{Ni}_2\text{O}_7\). Moreover, we’ve shown that the critical temperatures for these orbitals respond differently to doping. This is particularly enlightening because it serves as a practical experimental guidepost to figure out which electron orbitals primarily contribute to the emergence of superconductivity in this system.

To put it succinctly, we’ve provided a comprehensive understanding of the nickelate superconductors by exploring their behavior as doped SMG insulators. Our theory paints a detailed picture of how the inter-layer antiferromagnetic superexchange coupling plays a key role in promoting Cooper pairing and driving the material’s superconductivity. By advancing our understanding of this unique material, we’re opening new doors for experimental studies and setting the stage for a deeper understanding of high-temperature superconductivity. And in doing so, we’re taking one step closer to a world where the incredible potential of high-temperature superconductors can be fully realized.

(Written by OpenAI GPT4)

]]>Schrödinger’s cat, a thought experiment proposed by physicist Erwin Schrödinger, is a puzzling quantum superposition of states where a cat can be simultaneously dead and alive until observed. However, in our daily experiences, we never encounter such bizarre superpositions. Objects are either here or there, but never both. This raises the pressing question - how does the quantum world transition into the classical world we experience every day? This is what we refer to as the quantum-to-classical transition, and it’s a mystery that scientists have been grappling with for decades.

To tackle this problem, we sought the assistance of a powerful ally - Artificial Intelligence. We harnessed the power of generative language models, a type of artificial intelligence that’s been used to write human-like text, to model the ‘classical shadows’ of quantum states. These shadows, obtained from randomized local measurements on quantum many-body states, are the classical records of quantum states that disperse in the environment as random noise after the decoherence of the quantum system. However, by collecting these classical shadows of Schrödinger’s cat and processing them on a classical computer, we hope to decode the quantum nature of the cat.

The idea was to see if these language models could ‘understand’ and reproduce the quantum coherence encoded in the classical shadow data. Quantum coherence is a central feature of quantum mechanics and a key for quantum information processing. It describes the quantum superposition and interference between distinct states in a wave-like manner, encoded in the transition amplitude between the states of alive and dead cat. We find that for smaller quantum systems, a strong enough language model can learn to capture quantum coherence and understand the full quantum reality. However, as the size of the quantum system increases, the model quickly fails to decode the quantum coherence as it is encoded in high-order correlations whose variance grows exponentially with the system size. Therefore, the model can only infer the classical reality from the data.

This research bridges the gap between the arcane world of quantum mechanics and the familiar classical world, revealing that our perception of the universe’s quantum nature may be limited by our capacity to process classical information. As we continue to refine these models and techniques, we are slowly but surely uncovering the mysteries of the quantum world, bringing us closer to the day when we can fully comprehend and harness the power of quantum mechanics.

This is just the tip of the quantum iceberg! We invite you to dive deeper into the quantum realm with us by reading our full research paper at (arXiv: 2306.14838). Together, let’s explore the fascinating quantum-classical transition and how artificial intelligence can illuminate our path through this complex landscape!

(Written by OpenAI GPT4)

**GitHub repository**: EverettYou/EmergentClassicality (code and data)

**Talk recording**: [VIRTUAL] Emergent Classicality from Information Bottleneck (on *Machine Learning for Quantum Many-Body Systems* @ Perimeter Institute, June 2023)

Fermi liquids, which model the universal low-energy features of electrons in metals, have long perplexed researchers due to their remarkable stability under interactions. It was realized by the pioneering work of Bulmash, Hosur, Zhang and Qi (arXiv:1410.4202) that Fermi liquids can be viewed as Chern insulators (a type of topological insulator) in the phase space – a manifold spanned by both position and momentum coordinates. Our research further revealed that the topologically protected boundary modes of phase-space Chern insulators precisely correspond to the low-energy fermion modes near the Fermi surface, providing a profound topological explanation for the Fermi surface’s stability.

Traditionally, topological insulators are defined and classified in real space. However, our research extended this concept to the phase space, opening up a new frontier. The key challenge lies in the non-commutative geometry of phase space, where position and momentum coordinates are non-commuting observables according to quantum mechanics. This non-commutativity poses new challenges for defining and classifying phase-space Chern insulators. We developed non-perturbative approaches to resolve this non-commutativity, which enable us to describe the phase-space Chern insulator with the standard quantum field theory language, thus providing an accurate and consistent framework to analyze the classification problem.

We identified that the key to correctly classifying topological insulators in the phase space lies in an unconventional way of counting dimensions. We found that momentum space dimensions should be treated as “negative” dimensions and subtracted from the real space dimensions for classification purposes. Following this principle, we were able to show that Fermi surface anomalies are universally classified by (0+1)D fermionic SPT states —- a strikingly simple and elegant result.

The quest for understanding Fermi liquids has taken us to the exhilarating new frontier of phase space, and our journey has just begun. Classifying the Fermi surface anomaly is merely the first step. Based on the classification, we discovered the fascinating phenomenon of Fermi surface symmetric mass generation (SMG) (arXiv:2210.16304), where the Fermi surface can be fully gapped out into a trivial product state by non-perturbative interaction effects without breaking symmetry. This can only be achieved when the Fermi surface anomaly vanishes. The Fermi surface SMG has deeper implications to the nature of the pseudo-gap phase, which has been a long-standing puzzle in correlated electronic materials.

Our research not only contributes to the understanding of Fermi surface anomalies but also offers a more coherent and streamlined framework for studying them. Our works pave the way for further advances in condensed matter physics and inspires investigations into Fermi liquids, non-Fermi liquids, and topological phases.

（Written by OpenAI GPT4）

]]>Classical shadow tomography is an efficient approach to extract information about an unknown quantum state by measuring it in random basis. But the original proposal for classical shadow tomography had some limitations. It was limited to two measurement schemes: the single-qubit (local) Pauli measurement and the global Clifford measurement. The former is great for predicting local operators but inefficient for larger operators, while the latter is efficient for low-rank operators but not feasible on near-term quantum devices due to extensive gate overhead. The question arose: how can we go beyond these two limits and develop more flexible measurement schemes for classical shadow tomography?

In our recent work arXiv:2209.02093, we have developed a new scalable classical shadow tomography approach for generic randomized measurements that are implemented with finite-depth local Clifford random unitary circuits. What does that mean? Essentially, we have found a way to create more flexible measurement schemes to efficiently read out the quantum state on noisy intermediate-scale quantum (NISQ) devices.

This new method is exciting because it interpolates between the limits of Pauli and Clifford measurements, and is now called *shallow classical shadows*. It is great for predicting operators of various sizes, making it a more versatile approach to quantum state tomography. If you want to know more about shallow classical shadows, you can watch my talk Scalable Classical Shadow Tomography with Shallow Circuits and Quantum Dynamics - Yi-Zhuang You, UC San Diego at the KITP Program of Quantum Many-Body Dynamics and Noisy Intermediate-Scale Quantum Systems.

Overall, this new development in classical shadow tomography is a significant step forward in quantum information technology. It opens up new possibilities for predicting the properties of quantum systems with more flexible measurement schemes. As we continue to push the boundaries of quantum technology, it’s exciting to see how these innovations can help us unlock even more of its potential.

]]>SMG relies on the non-perturbative interaction effect of fermions, going beyond the conventional mean-field description of fermion mass generation in the Yukawa-Higgs theory. In the last few years, researchers have realized that the SMG has deep connections with interacting topological insulators, quantum anomaly cancellations, and deconfined quantum criticality. It also has strong implications for the lattice regularization for chiral gauge theories, which has been a long-standing problem in the lattice gauge theory.

To introduce the topic of SMG, I wrote a review paper with Juven Wang that summarizes the current numerical results, unifies current field theory understandings, and presents an overview of various features and applications of SMG.

At Paths to Quantum Field Theory 2022, I gave a talk about SMG, which you can watch on YouTube: Symmetric Mass Generation - Yi-Zhuang You.

]]>According to University of California San Diego Assistant Professor of Physics Yi-Zhuang You, the holographic universe can be thought of as a universe in virtual reality. All the information about this three-dimensional universe is projected from a two-dimensional screen of quantum pixels. The quantum physics on the two-dimensional screen gives rise to the quantum gravity behavior in the virtual universe. Between the two—the quantum boundary and the bulk gravity—lie dual theories known as the “holographic duality.”

To reveal this elusive duality, You and his team developed a novel machine-learning algorithm that enables artificial intelligence (AI) to learn from the boundary quantum theory and propose the corresponding bulk gravity dual. The results of their study are published in Physical Review Research, an American peer-reviewed scientific journal established in 1893 and published by the American Physical Society. According to the scientists, their outcome may shed light on a better understanding of the holographic duality, and it could result in new tools for exploring quantum gravity.

You and Hong-Ye Hu, a physics graduate student at UC San Diego, collaborated with Shuo-Hui Li and Lei Wang (Institute of Physics, Chinese Academy of Sciences, Beijing) to develop the machine-learning algorithm based on a deep artificial neural network—an interconnected group of nodes that mimic simple brain neurons. (arXiv:1903.00804)

“By arranging the artificial neurons in a hierarchical structure, the neural network is able to generate quantum field configurations as an artist creating a painting, level-by-level, from general composition to specific details. In this way, the artificial intelligence learns to identify the features at different scales in the quantum system and present them at different depths in the holographic bulk such that it can serve as a translator that can interpret the quantum theory in terms of the gravity theory and vice versa,” explained You. “The artificial intelligence not only learns to propose physics theories but also learns to find the connection between different theories that are dual to each other.”

According to You and Hu, at first the neural network “does not have a clue,” so it proposes arbitrary gravity theories. It generates quantum field configurations on the holographic boundary based on the hypothesized bulk gravity theory. The likelihood of the generated quantum field configuration is then evaluated according to the given field theory action, which provides an indication of how well the gravity theory is describing the boundary quantum physics. Such an indication will be fed back to train the neural network parameters.

“In iterative rounds of trial-and-error, the neural network gradually learns to modify its proposal of the gravity theory to improve the overall correctness of the consequent predictions,” explained Hu.

The structure of the neural network is inspired by the idea of renormalization group—an iterative approach to remove detail features in the physical system and extract overall structures at progressively larger scales—which gives the artificial intelligence the power to grasp and analyze the information at different length scales.

“One of our epiphanies in this research was to realize that if the process of renormalization were reversed, it would constitute a generative procedure, which could reconstruct the physical system in a hierarchical manner,” said You.

The researchers tested the algorithm on a quantum system with a large number of interacting particles. The quantum system is in a state that exhibits self-similarity, meaning that the system looks similar to itself from small to large scales. In this case, a new dimension will emerge in the holographic universe, which corresponds to the different scales to observe the quantum system.

“We are amazed to observe that a beautiful hyperbolic geometry of the holographic universe emerged in the neural network under training,” said Hu. “This is exciting because scientifically it shows how artificial intelligence can help scientists to understand how space-time can emerge from interacting quantum objects and to establish the holographic duality on the field theory level. In the long term, the space-time fluctuation could also be incorporated in the framework, which may lead to a possible quantum description of gravity.”

Another usage of the holographic duality established by the AI is to simulate the strong-interacting boundary quantum system from its holographic bulk.

“In many cases, the particles in the holographic universe are almost free, which makes the bulk gravity theory much easier to simulate compared to the boundary quantum theory. Therefore, our approach can help condensed matter physicists to simulate quantum materials, and find new phases of matter in the future,” said You.

The UC San Diego researchers are supported by a startup fund from the university. Li and Wang are supported by the National Natural Science Foundation of China (grant no. 11774398) and the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB28000000).

*(By Cynthia Dillon, reprinted from UCSD Physical Science News)*

A nice physical system to test these ideas is the deconfined quantum critical point (DQCP), which is an exotic quantum critical point that exists between two spontaneous symmetry breaking phases. At the DQCP, deconfined degrees of freedom, such as fractionalized spinons and emergent gauge fluctuations, appear. These phenomena can lead to the emergence of new symmetries, such as O(4) or SO(5), that involve the rotation of Neel and valence bond solid (VBS) order parameters to each other.

To confirm the presence of emergent symmetries at the DQCP, we search for associated emergent conserved currents. This is where the Noether theorem comes in handy. According to the theorem, each generator of a continuous symmetry corresponds to a distinct type of conserved current. If the proposed emergent symmetry is present, its associated emergent conserved current should be detected. But where do we find the signal of the emergent conserved current in the low-energy excitation spectrum, and how can we verify whether the observed current is conserved or not?

In a recent work arXiv:1811.08823, we identified the Neel-VBS current as the spin fluctuation at momentum \((\pi,0)\) and \((0,\pi)\) and checked its conservation by measuring its scaling dimension. The results confirmed the presence of emergent symmetry at the DQCP by measuring the associated emergent conserved current in the spin excitation spectrum.

This proposal applies to other scenarios, such as the low-dimensional analog of DQCP. In another recent study arXiv:1904.00021, the U(1)xU(1) emergent symmetry of the Ising-DQCP in (1+1)D was discovered, guiding the experimental search for the DQCP in quantum magnets. The Shastry-Sutherland magnet \(\text{Sr}\text{Cu}_2(\text{B}\text{O}_3)_2\) is one candidate material that could potentially realize the DQCP under pressure. In our latest work arXiv:1904.07266, we provided supporting evidence for the emergent O(4) symmetry and identified unique spectral features that originated from the corresponding emergent conserved currents. The experimental detection of these spectral signals would deepen our understanding of exotic quantum phase transitions and quantum spin liquid.

]]>While we are still far from a complete understanding of intelligence, recent developments in machine learning have allowed us to take a step in that direction. Specifically, we are interested in whether artificial neural networks can be used to discover physical concepts and laws from experimental data.

To illustrate this concept, let’s consider the case of quantum mechanics. Imagine if quantum mechanics had not yet been formulated, but physicists knew how to perform cold atom experiments to collect density distributions of Bose-Einstein condensate (BEC) in potential traps of different shapes. Could quantum mechanics be discovered as the most natural theory to explain the experimental data without any prior human bias? Or would the machine come up with an alternative form of quantum mechanics?

In our recent work arXiv:1901.11103, we show how a machine learning algorithm can discover quantum mechanics by learning to predict the BEC density given the potential profile. Remarkably, the machine is only exposed to the data of potentials and densities, yet the quantum wave function can emerge as latent variables in the neural network.

We are inspired by the development of machine translation, which is trained to map sequences of words from one language to another. The machine translator can develop a semantic space in its hidden layers, which holds the intrinsic representation of words or phrases that are universal to all languages. By analyzing the structure of the semantic space, we can gain understanding about the relations among words as perceived by the translator.

To apply this idea to the problem at hand, we treat the potential-to-density mapping as an example of sequence-to-sequence mapping that can be handled by the machine translation approach, such as the recurrent neural network. We train a recurrent neural network to translate the potential profile to the density profile along a one-dimensional trap. By learning to perform this translation, the machine gains intuitions about the underlying physics.

To extract what the machine translator has learned, we design a higher-level machine, called a knowledge distiller, to learn from the neural activations (hidden states) of the lower-level translator. The knowledge distiller is an auto-encoder incorporated in another recurrent neural network structure. Its task is to compress the hidden states generated by the translator at each step as much as possible without losing the prediction power to reconstruct subsequent hidden states. This allows the knowledge distiller to identify the essential variables.

Our study shows that the reconstruction loss of the knowledge distiller only increases abruptly when its latent space dimension is reduced below two. This implies that at least two real variables are required to describe the behavior of the potential-to-density translator. When we plot these two variables, they correspond to the real and imaginary parts of the quantum wave function (up to basis freedom). Further inspection of the update rules for these variables shows that they are governed by a recurrent relation that precisely matches the discrete version of the Schrödinger equation. Thus, knowledge about quantum mechanics emerges in the neural network.

Furthermore, if we relax the information bottleneck of the knowledge distiller, alternative forms of quantum mechanics, such as density functional theory, could also emerge, but it requires at least three real variables to describe. It is reassuring to know that the current formulation of quantum mechanics, in terms of the wave function and Schrödinger equation, is indeed the most parsimonious theory among all alternative theories of quantum mechanics that have been discovered in our neural network.

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