Fermion path integrals and topological phases

Edward Witten

Research output: Contribution to journalArticlepeer-review

220 Scopus citations

Abstract

Symmetry-protected topological (SPT) phases of matter have been interpreted in terms of anomalies, and it has been expected that a similar picture should hold for SPT phases with fermions. Here a description is given in detail of what this picture means for phases of quantum matter that can be understood via band theory and free fermions. The main examples considered are time-reversal invariant topological insulators and superconductors in two or three space dimensions. Along the way, the precise meaning of the statement that in the bulk of a 3D topological insulator, the electromagnetic θ angle is equal to π, is clarified.

Original languageEnglish (US)
Article number035001
JournalReviews of Modern Physics
Volume88
Issue number3
DOIs
StatePublished - Jul 13 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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