Anyonic symmetries and topological defects in Abelian topological phases: An application to the ADE classification

Mayukh Nilay Khan, Jeffrey C.Y. Teo, Taylor L. Hughes

Research output: Contribution to journalArticle

Abstract

We study symmetries and defects of a wide class of two-dimensional Abelian topological phases characterized by Lie algebras. We formulate the symmetry group of all Abelian topological field theories. The symmetries relabel quasiparticles (or anyons) but leave exchange and braiding statistics unchanged. Within the class of ADE phases, in particular, these anyonic symmetries have a natural origin from the Lie algebra. We classify one-dimensional gapped phases along the interface between identical topological states according to symmetries. This classification also applies to gapped edges of a wide range of fractional quantum spin Hall (QSH) states. We show that the edge states of the ADE QSH systems can be gapped even in the presence of time-reversal and charge-conservation symmetries. We distinguish topological point defects according to anyonic symmetries and bound quasiparticles. Although in an Abelian system, they surprisingly exhibit non-Abelian fractional Majorana-like characteristics from their fusion behavior.

Original languageEnglish (US)
Article number235149
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume90
Issue number23
DOIs
StatePublished - Dec 30 2014

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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