Dislocations in the Kitaev honeycomb model

We study the effects of introducing dislocations into the Kitaev honeycomb model [1]. In the gapped phase, dislocations are $Z_2$ ``twist defects'' associated with the transmutation of electric and magnetic excitations, studied previously in the context of $Z_N$ rotor models [2,3]. We show that each dislocation hosts one unpaired Majorana mode. As a consequence, twist defects have the statistics of Ising anyons. Because dislocations are confined, an additional phase is accumulated due to the change in system's energy during the braiding process. This means that the result of braiding can only be defined up to a phase. Therefore, twists are said to have projective non-Abelian statistics. \\[4pt][1] Alexei Kitaev, Annals of Physics \textbf{321}, 2 (2006) \\[0pt][2] Hector Bombin, Phys. Rev. Lett. \textbf{105}, 030403 (2010) \\[0pt][3] Yi-Zhuang You and Xiao-Gang Wen, Phys. Rev. B \textbf{86}, 161107 (2012)