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

statistics of dislocation defects in a Z[subscript N] rotor model. " Physical Review B 86.16 (2012). Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Non-Abelian statistics is a phenomenon of topologically protected non-Abelian geometric phases as we exchange quasiparticle excitations. Here 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 √ 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 N rotor model. These types of non-Abelian anyons can be viewed as a generalization of the Majorana zero modes. Introduction. Searching for Majorana fermions (or more precisely, Majorana zero modes) in condensed matter systems has attracted increasing research interests recently. 1–10 But what is really the Majorana zero mode? In fact, the so-called " Majorana zero mode " is actually a phenomenon of topologically protected degeneracy 11,12 in the presence of certain topological defects [such as vortices in two-dimensional (2D) p x + ip y superconductors 2,3 ]. In the race for finding Majorana zero modes, much attention has been paid to the fermion systems. 4–10 However the boson/spin systems also have topologically protected degeneracies,