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

Mayukh Nilay Khan, Jeffrey C. Y. Teo, and Taylor L. Hughes
Phys. Rev. B 90, 235149 – Published 30 December 2014

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.

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  • Received 26 April 2014
  • Revised 25 November 2014

DOI:https://doi.org/10.1103/PhysRevB.90.235149

©2014 American Physical Society

Authors & Affiliations

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

  • Department of Physics, Institute for Condensed Matter Theory, University of Illinois at Urbana-Champaign, Illinois 61801, USA

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Issue

Vol. 90, Iss. 23 — 15 December 2014

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