Interactions, Entanglement, and Anomalies in Topological Semimetals
| dc.contributor.author | Yang, Lei | |
| dc.date.accessioned | 2023-08-04T15:15:01Z | |
| dc.date.available | 2023-08-04T15:15:01Z | |
| dc.date.issued | 2023-08-04 | |
| dc.date.submitted | 2023-08-01 | |
| dc.description.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. | en |
| dc.identifier.uri | http://hdl.handle.net/10012/19652 | |
| dc.language.iso | en | en |
| dc.pending | false | |
| dc.publisher | University of Waterloo | en |
| dc.subject | topological semimetals | en |
| dc.subject | phases of matter | en |
| dc.subject | metals | en |
| dc.subject | LSM theorems | en |
| dc.subject | quantum phases of matter | en |
| dc.subject | quantum entanglement | en |
| dc.subject | weyl semimetal | en |
| dc.subject | dirac semimetal | en |
| dc.subject | quantum anomaly | en |
| dc.subject | topological response | en |
| dc.subject | strong interactions | en |
| dc.subject | vortex condensation | en |
| dc.subject | quantum information | en |
| dc.subject | crystalline defects | en |
| dc.subject | translation symmetry | en |
| dc.subject | rotation symmetry | en |
| dc.subject | dislocations | en |
| dc.subject | disclinations | en |
| dc.subject | Luttingers theorem | en |
| dc.subject | symmetry-protected topological phases | en |
| dc.subject | SPT | en |
| dc.subject | SRE | en |
| dc.subject | topological insulators | en |
| dc.subject | topological quantum field theory | en |
| dc.subject | chiral anomaly | en |
| dc.subject | crystalline momentum | en |
| dc.subject | TQFT | en |
| dc.subject | Landau levels | en |
| dc.subject | strongly-correlated electrons | en |
| dc.subject | condensed matter | en |
| dc.subject | topological phases of matter | en |
| dc.subject | topology and symmetry | en |
| dc.title | Interactions, Entanglement, and Anomalies in Topological Semimetals | en |
| dc.type | Doctoral Thesis | en |
| uws-etd.degree | Doctor of Philosophy | en |
| uws-etd.degree.department | Physics and Astronomy | en |
| uws-etd.degree.discipline | Physics | en |
| uws-etd.degree.grantor | University of Waterloo | en |
| uws-etd.embargo.terms | 0 | en |
| uws.contributor.advisor | Burkov, Anton | |
| uws.contributor.advisor | Wang, Chong | |
| uws.contributor.affiliation1 | Faculty of Science | en |
| uws.peerReviewStatus | Unreviewed | en |
| uws.published.city | Waterloo | en |
| uws.published.country | Canada | en |
| uws.published.province | Ontario | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |