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arXiv · 1202.3120

Braiding statistics approach to symmetry-protected topological phases

Michael Levin·Zheng-Cheng Gu
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Abstract

We construct a 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.

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Michael Levin, Zheng-Cheng Gu. 2012-09-27. Braiding statistics approach to symmetry-protected topological phases. https://doi.org/10.1103/physrevb.86.115109

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