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Title: Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators

Journal Article · · Physical Review. X
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Here, 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 Z2 topological order and a symmetry group of the form G=U(1)xG', 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)×ZT2 and G=U(1)×ZP2, where ZT2 and ZP2 are time-reversal and d=2 reflection symmetry, respectively.

Research Organization:
Univ. of Colorado, Boulder, CO (United States)
Sponsoring Organization:
USDOE
Grant/Contract Number:
FG02-10ER46686; SC0003910; SC0014415
OSTI ID:
1328821
Alternate ID(s):
OSTI ID: 1361687
Journal Information:
Physical Review. X, Journal Name: Physical Review. X Vol. 6 Journal Issue: 4; ISSN 2160-3308
Publisher:
American Physical SocietyCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 25 works
Citation information provided by
Web of Science

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