Fluxfusion anomaly test and bosonic topological crystalline insulators
Here, we introduce a method, dubbed the fluxfusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in twodimensional symmetryenriched 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 symmetryprotected 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}more »
 Authors:

^{[1]};
^{[2]}
 Univ. of Colorado, Boulder, CO (United States)
 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Publication Date:
 Grant/Contract Number:
 SC0014415; FG0210ER46686
 Type:
 Published Article
 Journal Name:
 Physical Review. X
 Additional Journal Information:
 Journal Volume: 6; Journal Issue: 4; Journal ID: ISSN 21603308
 Publisher:
 American Physical Society
 Research Org:
 Univ. of Colorado, Boulder, CO (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 36 MATERIALS SCIENCE
 OSTI Identifier:
 1328821
 Alternate Identifier(s):
 OSTI ID: 1361687
Hermele, Michael, and Chen, Xie. Fluxfusion anomaly test and bosonic topological crystalline insulators. United States: N. p.,
Web. doi:10.1103/PhysRevX.6.041006.
Hermele, Michael, & Chen, Xie. Fluxfusion anomaly test and bosonic topological crystalline insulators. United States. doi:10.1103/PhysRevX.6.041006.
Hermele, Michael, and Chen, Xie. 2016.
"Fluxfusion anomaly test and bosonic topological crystalline insulators". United States.
doi:10.1103/PhysRevX.6.041006.
@article{osti_1328821,
title = {Fluxfusion anomaly test and bosonic topological crystalline insulators},
author = {Hermele, Michael and Chen, Xie},
abstractNote = {Here, we introduce a method, dubbed the fluxfusion anomaly test, to detect certain anomalous symmetry fractionalization patterns in twodimensional symmetryenriched 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 symmetryprotected 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 timereversal and d=2 reflection symmetry, respectively.},
doi = {10.1103/PhysRevX.6.041006},
journal = {Physical Review. X},
number = 4,
volume = 6,
place = {United States},
year = {2016},
month = {10}
}