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Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions

Cheng, Meng and Gu, Zheng-Cheng (2014) Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions. Physical Review Letters, 112 (14). Art. No. 141602. ISSN 0031-9007. https://resolver.caltech.edu/CaltechAUTHORS:20140819-094714779

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Abstract

It has been shown that the symmetry-protected topological (SPT) phases with finite Abelian symmetries can be described by Chern-Simons field theory. We propose a topological response theory to uniquely identify the SPT orders, which allows us to obtain a systematic scheme to classify bosonic SPT phases with any finite Abelian symmetry group. We point out that even for finite Abelian symmetry, there exist bosonic SPT phases beyond the current Chern-Simons theory framework. We also apply the theory to fermionic SPT phases with Z_m symmetry and find the classification of SPT phases depends on the parity of m : for even m there are 2m classes, m out of which is intrinsically fermionic SPT phases and cannot be realized in any bosonic system. Finally we propose a classification scheme of fermionic SPT phases for any finite, Abelian symmetry.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevLett.112.141602DOIArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.141602PublisherArticle
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.141602#supplementalPublisherSupplemental Material
http://arxiv.org/abs/1302.4803arXivArticle
Additional Information:© 2014 American Physical Society. Received 1 March 2013; Revised manuscript received 29 October 2013; Published 9 April 2014. M. C. thanks Lukasz Fidkowski, Chetan Nayak, Zhenghan Wang, and Juven Wang for insightful discussions. Z.-C. G is supported in part by Frontiers Center with support from the Gordon and Betty Moore Foundation.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Issue or Number:14
Classification Code:PACS numbers: 11.15.Yc
Record Number:CaltechAUTHORS:20140819-094714779
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140819-094714779
Official Citation:Cheng, M., & Gu, Z.-C. (2014). Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions. Physical Review Letters, 112(14), 141602.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:48677
Collection:CaltechAUTHORS
Deposited By: Joanne McCole
Deposited On:19 Aug 2014 18:13
Last Modified:03 Oct 2019 07:06

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