Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model

TL;DR

This paper introduces a Z_N rotor model where lattice dislocation defects exhibit non-Abelian statistics, leading to topologically protected degeneracy and Berry phases, resembling non-Abelian anyons like Majorana modes.

Contribution

The study constructs a self-dual Z_N gauge theory model demonstrating dislocation defects with non-Abelian statistics, a novel insight into topological quantum phenomena.

Findings

Dislocations produce topologically protected degeneracy.

Exchanging dislocations yields projective non-Abelian Berry phases.

Dislocations act as generalizations of Majorana zero modes.

Abstract

Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, we construct a Z_N rotor model that realizes a self-dual Z_N Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension sqrt(N). Exchanging dislocations can produces topologically protected projective non-Abelian Berry phases. The dislocations, as projective non-Abelian anyons can be viewed as a generalization of the Majorana zero modes.