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

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Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, we construct a Zₙ rotor model that realizes a self-dual Zₙ 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.