TY - JOUR
T1 - Anomaly Indicators for Time-Reversal Symmetric Topological Orders
AU - Wang, Chenjie
AU - Levin, Michael
PY - 2017/9/29
Y1 - 2017/9/29
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 apreviously 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 apreviously 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.
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U2 - 10.1103/PhysRevLett.119.136801
DO - 10.1103/PhysRevLett.119.136801
M3 - RGC 21 - Publication in refereed journal
VL - 119
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 13
M1 - 136801
ER -