The Noether theorem is a profound theorem in physics, relating continuous symmetries to conservation laws. The German mathematician Emmy Noether first proved it. Some famous examples include space-time translation symmetry and momentum-energy conservation, rotation symmetry and angular momentum conservation, internal U(1) symmetry and charge conservation. In quantum many-body systems, the discussion of symmetry can be more involved. For example, new symmetry that does not exist in the system can even emerge at low energy. Such a phenomenon generally occurs when the symmetry breaking terms are all irrelevant under the renormalization group (RG) flow in the field theory description. Do emergent symmetries also lead to emergent conservation laws?
The emergent phenomenon is a central theme of condensed matter physics. Not only matter and forces can be emergent, spacetime and gravity could also be emergent. These exciting ideas are being actively explored in the frontier of physics research. But wait a moment, aren’t all these physics theories themselves also emergent phenomena? This is an interesting idea. Physics theories are indeed collective neural activations in human’s brain. It is unclear how the ideas of physics emerge in the neural network of a physicist, or more generally, in the physics community. Understanding the universal principles of emergent intelligence in complex networks should be one important goal of science.
When two periodic lattices lie on top of each other with a relative twist or a mismatched lattice constant, they can interfere to create a Moire pattern. As shown in the following figure, a Moire pattern has a spatial structure on a larger scale than either of the lattice along. The (quasi)periodic pattern forms a larger lattice, known as the Moire superlattice. Experimentally, the Moire superlattice can be realized by stacking 2D materials together, including graphene, hexagonal boron nitride (hBN), molybdenum disulfide and many others. Exciting new physics can emerge on Moire superlattices, including Mott insulators, unconventional superconductors and possibly new topological phases.
Quantum information dynamics is an emerging field that ties several topics together, including non-equilibrium and driven quantum systems, many-body localization and thermalization, quantum chaos and black holes, tensor network holography. Traditionally, one may think that physics is about the dynamics of matter and spacetime. Extending our scope to the dynamics of quantum information is a new trend, which in turn deepen our understanding of the dynamics of matter and spacetime.
The holographic duality (AdS/CFT) was originally proposed as the correspondence between a -dimensional quantum field theory and a -dimensional quantum gravity theory. The information about the space-time geometry in the higher-dimensional holographic bulk is encoded in the quantum many-body dynamics on the lower-dimensional holographic boundary, hence the name “holography”. The holographic duality reveals a deep connection between quantum entanglement and space-time geometry: “Entanglement is the fabric of space-time”, said Brain Swingle on Quantum Magazine.