TY - JOUR

T1 - Topological central charge from Berry curvature

T2 - Gravitational anomalies in trial wave functions for topological phases

AU - Bradlyn, Barry

AU - Read, N.

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/4/20

Y1 - 2015/4/20

N2 - We show that the topological central charge of a topological phase can be directly accessed from the ground-state wave functions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wave functions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U(1) gauge anomaly.

AB - We show that the topological central charge of a topological phase can be directly accessed from the ground-state wave functions for a system on a surface as a Berry curvature produced by adiabatic variation of the metric on the surface, at least up to addition of another topological invariant that arises in some cases. For trial wave functions that are given by conformal blocks (chiral correlation functions) in a conformal field theory (CFT), we carry out this calculation analytically, using the hypothesis of generalized screening. The topological central charge is found to be that of the underlying CFT used in the construction, as expected. The calculation makes use of the gravitational anomaly in the chiral CFT. It is also shown that the Hall conductivity can be obtained in an analogous way from the U(1) gauge anomaly.

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U2 - 10.1103/PhysRevB.91.165306

DO - 10.1103/PhysRevB.91.165306

M3 - Article

AN - SCOPUS:84929190371

SN - 1098-0121

VL - 91

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 16

M1 - 165306

ER -