Projective non-Abelian statistics of dislocation defects in a Z[subscript N] rotor model

Abstract

Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here we construct a Z[subscript N] rotor model that realizes a self-dual Z[subscript 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 √N. Exchanging dislocations can produce topologically protected projective non-Abelian geometric phases. Therefore, we discover a kind of (projective) non-Abelian anyon that appears as the dislocations in an Abelian Z[subscript N] rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes.