Interactions, Entanglement, and Anomalies in Topological Semimetals
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Date
2023-08-04
Authors
Yang, Lei
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Publisher
University of Waterloo
Abstract
Topology and symmetry have become one of the backbones of modern condensed matter physics. These concepts play a large role in determining the possible effects of interactions and entanglement in both gapped and gapless systems. Gapped systems possess a well-developed description via topological quantum field theory (TQFT) that has given rise to many exciting concepts such as topological orders. However gapless systems are far less well-understood in the context of topology as they cannot be described by a simple TQFT due to the presence of local degrees of freedom at low energy. In this thesis I will explore these concepts in the framework of topological response in gapless systems with a focus on 3+1d Weyl and Dirac semimetallic systems. I develop a theory of unquantized topological response, as opposed to the usual quantized response of gapped systems, and explore the effects of strong interaction in the presence of these terms. I show that the associated unquantized topological quantities arise from crystalline symmetries such as discrete translations and rotations. Inspired by the topological crystalline quantity of momentum, I also develop a general theorem involving just discrete translation symmetry that can distinguish long-range entangled states from short-range entangled states. Such a statement can be seen as a generalisation of the well-known Lieb-Schultz-Mattis theorems and many are shown to be consequences from the pure translation theorem that I develop here.
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Keywords
topological semimetals, phases of matter, metals, LSM theorems, quantum phases of matter, quantum entanglement, weyl semimetal, dirac semimetal, quantum anomaly, topological response, strong interactions, vortex condensation, quantum information, crystalline defects, translation symmetry, rotation symmetry, dislocations, disclinations, Luttingers theorem, symmetry-protected topological phases, SPT, SRE, topological insulators, topological quantum field theory, chiral anomaly, crystalline momentum, TQFT, Landau levels, strongly-correlated electrons, condensed matter, topological phases of matter, topology and symmetry