Braiding statistics approach to symmetry-protected topological phases

Michael Levin, Zheng Cheng Gu

Research output: Contribution to journalArticlepeer-review

317 Scopus citations


We construct a two-dimensional (2D) quantum spin model that realizes an Ising paramagnet with gapless edge modes protected by Ising symmetry. This model provides an example of a "symmetry-protected topological phase." We describe a simple physical construction that distinguishes this system from a conventional paramagnet: We couple the system to a Z 2 gauge field and then show that the π-flux excitations have different braiding statistics from that of a usual paramagnet. In addition, we show that these braiding statistics directly imply the existence of protected edge modes. Finally, we analyze a particular microscopic model for the edge and derive a field theoretic description of the low energy excitations. We believe that the braiding statistics approach outlined in this paper can be generalized to a large class of symmetry-protected topological phases.

Original languageEnglish
Article number115109
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number11
StatePublished - 10 Sep 2012
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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