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Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators

Hermele, Michael and Chen, Xie (2016) Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators. Physical Review X, 6 (4). Art. No. 041006. ISSN 2160-3308. doi:10.1103/PhysRevX.6.041006.

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We introduce a method, dubbed the flux-fusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in two-dimensional symmetry-enriched topological (SET) phases. We focus on bosonic systems with ℤ_2 topological order and a symmetry group of the form G=U(1)⋊G′, where G′ is an arbitrary group that may include spatial symmetries and/or time reversal. The anomalous fractionalization patterns we identify cannot occur in strictly d=2 systems but can occur at surfaces of d=3 symmetry-protected topological (SPT) phases. This observation leads to examples of d=3 bosonic topological crystalline insulators (TCIs) that, to our knowledge, have not previously been identified. In some cases, these d=3 bosonic TCIs can have an anomalous superfluid at the surface, which is characterized by nontrivial projective transformations of the superfluid vortices under symmetry. The basic idea of our anomaly test is to introduce fluxes of the U(1) symmetry and to show that some fractionalization patterns cannot be extended to a consistent action of G′ symmetry on the fluxes. For some anomalies, this can be described in terms of dimensional reduction to d=1 SPT phases. We apply our method to several different symmetry groups with nontrivial anomalies, including G=U(1)×ℤ^T_2 and G=U(1)×ℤ^P_2, where ℤ^T_2 and ℤ^P_2 are time-reversal and d=2 reflection symmetry, respectively.

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Alternate Title:Bosonic topological crystalline insulators and anomalous symmetry fractionalization via the flux-fusion anomaly test
Additional Information:© 2016 The Authors. 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 13 August 2015; revised manuscript received 16 June 2016; published 13 October 2016) M. H. is grateful to T. Senthil for several conversations that helped inspire some of these ideas, and to Olexei Motrunich for a useful discussion. X. C. would like to thank Meng Cheng for helpful discussions. We thank Zhenghan Wang for useful correspondence. M. H. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under Grant No. DE-FG02-10ER46686 and subsequently under Grant No. DE-SC0014415, and by Simons Foundation Grant No. 305008 (sabbatical support). X. C. is supported by the Caltech Institute for Quantum Information and Matter and the Walter Burke Institute for Theoretical Physics. Publication of this article was funded in part by the University of Colorado Boulder Libraries Open Access Fund.
Group:Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Department of Energy (DOE)DE-FG02-10ER46686
Department of Energy (DOE)DE-SC0014415
Simons Foundation305008
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
University of ColoradoUNSPECIFIED
Issue or Number:4
Record Number:CaltechAUTHORS:20160623-123437341
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Official Citation:Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators Michael Hermele and Xie Chen Phys. Rev. X 6, 041006
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:68637
Deposited By: Jacquelyn O'Sullivan
Deposited On:27 Jun 2016 16:19
Last Modified:11 Nov 2021 04:02

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