Anomalies in bosonic symmetry-protected topological edge theories: Connection to symbols and a method of calculation

Kyle Kawagoe, Michael Levin

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We describe a systematic procedure for determining the identity of a 2D bosonic symmetry-protected topological (SPT) phase from the properties of its edge excitations. Our approach applies to general bosonic SPT phases with either unitary or antiunitary symmetries, and with either continuous or discrete symmetry groups, with the only restriction being that the symmetries must be on-site. Concretely, our procedure takes a bosonic SPT edge theory as input, and produces an element of the cohomology group . This element can be interpreted as either a label for the bulk 2D SPT phase or a label for the anomaly carried by the SPT edge theory. The basic idea behind our approach is to compute the symbol associated with domain walls in a symmetry-broken edge theory; this domain-wall symbol is precisely the anomaly we wish to compute. We demonstrate our approach with several SPT edge theories, including both lattice models and continuum field theories.

Original languageEnglish
Article number115156
JournalPhysical Review B
Volume104
Issue number11
DOIs
StatePublished - 15 Sep 2021
Externally publishedYes

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