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Towards Gauging Time-Reversal Symmetry: A Tensor Network Approach

Chen, Xie and Vishwanath, Ashvin (2015) Towards Gauging Time-Reversal Symmetry: A Tensor Network Approach. Physical Review X, 5 (4). Art. No. 041034. ISSN 2160-3308. http://resolver.caltech.edu/CaltechAUTHORS:20160104-140519845

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Abstract

It is well known that unitary symmetries can be “gauged,” i.e., defined to act in a local way, which leads to a corresponding gauge field. Gauging, for example, the charge-conservation symmetry leads to electromagnetic gauge fields. It is an open question whether an analogous process is possible for time reversal which is an antiunitary symmetry. Here, we discuss a route to gauging time-reversal symmetry that applies to gapped quantum ground states that admit a tensor network representation. The tensor network representation of quantum states provides a notion of locality for the wave function coefficient and hence a notion of locality for the action of complex conjugation in antiunitary symmetries. Based on that, we show how time reversal can be applied locally and also describe time-reversal symmetry twists that act as gauge fluxes through nontrivial loops in the system. As with unitary symmetries, gauging time reversal provides useful access to the physical properties of the system. We show how topological invariants of certain time-reversal symmetric topological phases in D=1, 2 are readily extracted using these ideas.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevX.5.041034DOIArticle
http://journals.aps.org/prx/abstract/10.1103/PhysRevX.5.041034PublisherArticle
Additional Information:Published by the American Physical Society. This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. (Received 20 April 2015; revised manuscript received 4 November 2015; published 30 November 2015) X. C. wants to thank Xiao-Gang Wen, Alexei Kitaev, Lukasz Fidkowski, Max Metlitski, and Mike Zaletel for very helpful discussions. X. C. is supported by the Miller Institute for Basic Research in Science at UC Berkeley, the Caltech Institute for Quantum Information and Matter, and the Walter Burke Institute for Theoretical Physics. A. V. is supported by NSF DMR 0645691.
Group:IQIM, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Miller Institute for Basic Research in ScienceUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
NSFDMR-0645691
Record Number:CaltechAUTHORS:20160104-140519845
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20160104-140519845
Official Citation:Towards Gauging Time-Reversal Symmetry: A Tensor Network Approach Xie Chen and Ashvin Vishwanath Phys. Rev. X 5, 041034 – Published 30 November 2015
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:63340
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:04 Jan 2016 22:54
Last Modified:04 Jan 2016 22:54

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