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Symmetry Fractionalization in Two Dimensional Topological Phases

Chen, Xie (2017) Symmetry Fractionalization in Two Dimensional Topological Phases. Reviews in Physics, 2 . pp. 3-18. ISSN 2405-4283. http://resolver.caltech.edu/CaltechAUTHORS:20161107-083133279

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Abstract

Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional charges while the electrons making up the system have charge one. An important question is to understand what symmetry fractionalization (SF) patterns are possible given different types of topological order and different global symmetries. A lot of progress has been made recently in classifying the SF patterns, providing deep insight into the strongly correlated experimental signatures of systems like spin liquids and topological insulators. We review recent developments on this topic. First, it was shown that the SF patterns need to satisfy some simple consistency conditions. More interestingly, it was realized that some seemingly consistent SF patterns are actually ‘anomalous’, i.e. they cannot be realized in strictly 2D systems. We review various methods that have been developed to detect such anomalies. Applying such an understanding to 2D spin liquid allows one to enumerate all potentially realizable SF patterns and propose numerical and experimental probing methods to distinguish them. On the other hand, the anomalous SF patterns were shown to exist on the surface of 3D systems and reflect the nontrivial order in the 3D bulk. We review examples of this kind where the bulk states are topological insulators, topological superconductors, or have other symmetry protected topological orders.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/j.revip.2017.02.002DOIArticle
http://www.sciencedirect.com/science/article/pii/S2405428317300023PublisherArticle
https://arxiv.org/abs/1606.07569arXivDiscussion Paper
Additional Information:© 2017 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Available online 20 February 2017. XC is grateful to Parsa Bonderson, Meng Cheng, Lukasz Fidkowski, Mike Hermele, Anton Kapustin, Yuan-Ming Lu, Joseph Maciejko, Ryan Thorngren, Senthil Todadri, Ashvin Vishwanath, Chong Wang and Mike Zaletel for carefully reading the paper and providing valuable feedback. XC is supported by the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Record Number:CaltechAUTHORS:20161107-083133279
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161107-083133279
Official Citation:Xie Chen, Symmetry fractionalization in two dimensional topological phases, Reviews in Physics, Volume 2, November 2017, Pages 3-18, ISSN 2405-4283, https://doi.org/10.1016/j.revip.2017.02.002. (http://www.sciencedirect.com/science/article/pii/S2405428317300023)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71756
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Nov 2016 20:07
Last Modified:28 Jun 2017 16:16

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