Topological central charge from Berry curvature: Gravitational anomalies in trial wave functions for topological phases

Barry Bradlyn, N. Read

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Article number165306
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume91
Issue number16
DOIs
StatePublished - Apr 20 2015
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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