Field theories for gauged symmetry-protected topological phases: Non-Abelian anyons with Abelian gauge group Z2 - 3

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Authors

Colleges, School and Institutes

External organisations

  • PRINCETON UNIVERSITY

Abstract

Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting even for Abelian gauge groups, the goal of this work is to fill the gap in the literature, especially for a selection of DW models with Abelian gauge groups but non-Abelian topological order. Particularly, we focus on the appearance of non-Abelian statistics in type-III twisted DW theories with Abelian gauge groups Z2 - 3. There are only 22 distinguishable line operators, and their fusion rules and correlation functions are calculated. The flux insertion operators have quantum dimension 2, which clearly demonstrates the non-Abelian topological order of type-III twisted DW theories.

Details

Original languageEnglish
Article number035131
JournalPhysical Review B
Volume95
Issue number3
Publication statusPublished - 19 Jan 2017

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