Topological phenomena in condensed matter physics
Abstract/Contents
- Abstract
- In this thesis, we study the topological phenomena in 2+1 dimensional topologically ordered states with additional extrinsic structures. One type of extrinsic structures we will study in this thesis is extrinsic defect. We first introduce the conceptual scheme of extrinsic twist defects which are point-like defects associated with symmetries of the 2+1 dimensional topological states. We explicitly study several classes of examples. In particular, we study several class the projective non-Abelian braiding statistics of the twist defects which are fundamentally different from the statistics of intrinsic excitations in topological systems. We also find an example where the projective non-Abelian statistics of twist defects can be exploited for universal topological quantum computation, while the host state itself is not suitable for this purpose. Apart from twist defects, extrinsic defects in 2+1 dimensional topological states can take various other forms including line-like defects and point-like defects. For 2+1 dimensional Abelian topological states, we establish a general classification of all line-like and point-like defects. We develop a general method to analyze the quantum dimensions of all the point-like defects, a general understanding of their localized "parafermion" zero modes, and study the projective non-Abelian statistics of them. Another type of extrinsic structure this thesis focuses on is the layering structure of 2+1 dimensional topological states. We propose a general formalism for constructing a large class of 3+1 dimensional topological states by stacking layers of 2+1 dimensional topological states and introducing coupling between them. Using this construction, we can study interesting topological phenomena in 3+1 dimensions, including surface topological orders and 3+1 dimensional topological orders. As an interesting consequence of this construction, we obtain example systems with nontrivial braiding statistics between string-like excitations. In addition to studying the string-string braiding in the example system, we propose a generic topological field theory description which can capture both string-particle and string-string braiding statistics. Lastly, we provide a proof of a general identity for Abelian string statistics, and discuss an example system with non-Abelian strings.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2016 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Jian, Chaoming |
|---|---|
| Associated with | Stanford University, Department of Physics. |
| Primary advisor | Qi, Xiaoliang |
| Thesis advisor | Qi, Xiaoliang |
| Thesis advisor | Kivelson, Steven |
| Thesis advisor | Raghu, Srinivas, 1978- |
| Thesis advisor | Zhang, Shoucheng |
| Advisor | Kivelson, Steven |
| Advisor | Raghu, Srinivas, 1978- |
| Advisor | Zhang, Shoucheng |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Chaoming Jian. |
|---|---|
| Note | Submitted to the Department of Physics. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2016. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2016 by Chaoming Jian
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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