Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators
Abstract
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 andmore »
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Colorado, Boulder, CO (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1328821
- Alternate Identifier(s):
- OSTI ID: 1361687
- Grant/Contract Number:
- FG02-10ER46686; SC0003910; SC0014415
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. X
- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 6 Journal Issue: 4; Journal ID: ISSN 2160-3308
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 36 MATERIALS SCIENCE
Citation Formats
Hermele, Michael, and Chen, Xie. Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators. United States: N. p., 2016.
Web. doi:10.1103/PhysRevX.6.041006.
Hermele, Michael, & Chen, Xie. Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators. United States. https://doi.org/10.1103/PhysRevX.6.041006
Hermele, Michael, and Chen, Xie. Thu .
"Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators". United States. https://doi.org/10.1103/PhysRevX.6.041006.
@article{osti_1328821,
title = {Flux-Fusion Anomaly Test and Bosonic Topological Crystalline Insulators},
author = {Hermele, Michael and Chen, Xie},
abstractNote = {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.},
doi = {10.1103/PhysRevX.6.041006},
journal = {Physical Review. X},
number = 4,
volume = 6,
place = {United States},
year = {Thu Oct 13 00:00:00 EDT 2016},
month = {Thu Oct 13 00:00:00 EDT 2016}
}
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