TY - JOUR
T1 - Anomaly Indicators for Time-Reversal Symmetric Topological Orders
AU - Wang, Chenjie
AU - Levin, Michael
N1 - Funding Information:
We thank E. Berg, M. Cheng, M. Metlitski, and Y. Qi for enlightening discussions. In particular, C. W. would like to thank M. Metlitski for kindly teaching him various aspects of surface topological orders of 3D topological insulators and superconductors. We also thank M. Metlitski for bringing the example of time-reversal symmetric double-layer topological order to our attention. M. L. is supported in part by NSF DMR-1254741. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.
Publisher Copyright:
© 2017 American Physical Society.
PY - 2017/9/26
Y1 - 2017/9/26
N2 - Some time-reversal symmetric topological orders are anomalous in that they cannot be realized in strictly two-dimensional systems; instead, they can only be realized on the surface of three-dimensional symmetry-protected topological phases. We propose two quantities, which we call anomaly indicators, that can detect if a time-reversal symmetric topological order is anomalous in this sense. Both anomaly indicators are expressed in terms of the quantum dimensions, topological spins, and time-reversal properties of the anyons in the given topological order. The first indicator, η2, applies to bosonic systems while the second indicator, ηf, applies to fermionic systems in the DIII class. We conjecture that η2, together with a previously known indicator η1, can detect the two known Z2 anomalies in the bosonic case, while ηf can detect the Z16 anomaly in the fermionic case.
AB - Some time-reversal symmetric topological orders are anomalous in that they cannot be realized in strictly two-dimensional systems; instead, they can only be realized on the surface of three-dimensional symmetry-protected topological phases. We propose two quantities, which we call anomaly indicators, that can detect if a time-reversal symmetric topological order is anomalous in this sense. Both anomaly indicators are expressed in terms of the quantum dimensions, topological spins, and time-reversal properties of the anyons in the given topological order. The first indicator, η2, applies to bosonic systems while the second indicator, ηf, applies to fermionic systems in the DIII class. We conjecture that η2, together with a previously known indicator η1, can detect the two known Z2 anomalies in the bosonic case, while ηf can detect the Z16 anomaly in the fermionic case.
UR - http://www.scopus.com/inward/record.url?scp=85030167431&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.119.136801
DO - 10.1103/PhysRevLett.119.136801
M3 - Article
C2 - 29341704
AN - SCOPUS:85030167431
VL - 119
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 13
M1 - 136801
ER -