Interactions, Entanglement, and Anomalies in Topological Semimetals
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.
Collections
Cite this version of the work
Lei Yang
(2023).
Interactions, Entanglement, and Anomalies in Topological Semimetals. UWSpace.
http://hdl.handle.net/10012/19652
Other formats
Related items
Showing items related by title, author, creator and subject.
-
Topological Quantum Computation and Protected Gates
Sijher, Sumit (University of Waterloo, 2015-12-22)This thesis serves to give a mathematical overview of topological quantum computation and to apply the theory to characterize desirable fault-tolerant operations called protected gates. Topological quantum computation is ... -
Hopf 2-Algebras: Homotopy Higher Symmetries in Physics
Chen, Hank (University of Waterloo, 2024-06-26)The theory of Hopf algebras and quantum groups have led to very rich and interesting developments in both mathematics and physics. In particular, they are known to play crucial roles in the interplay between 3d topological ... -
Topological and superconducting properties of Weyl and Dirac metals
Bednik, Grigory (University of Waterloo, 2018-08-30)In this work we explore superconductivity and surface states in topological semimetals. We start from general overview of basic properties of topological semimetals. We review general concepts of Chern insulators, their ...