Braiding statistics approach to symmetry-protected topological phases

TL;DR

This paper introduces a 2D quantum spin model demonstrating a symmetry-protected topological phase with gapless edge modes, distinguished by unique braiding statistics of -flux excitations, and provides a generalizable approach to such phases.

Contribution

It presents a novel braiding statistics framework for identifying and analyzing symmetry-protected topological phases in quantum spin systems.

Findings

Constructed a 2D model with protected edge modes

Coupled the system to a Z_2 gauge field to reveal braiding differences

Derived a field theory describing low-energy edge excitations

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 \pi-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.