Non-abelian anyons on dislocations in Kitaev's honeycomb spin liquid

Kitaev's honeycomb model [1] is an exactly solvable model of a quantum spin liquid. Its gapped phase exhibits $Z_2$ topological order and has low-energy excitations in the form of $Z_2$ fluxes (visons). Previous studies [2] have demonstrated that even trivial lattice defects such as vacancies induce free magnetic moments with peculiar properties. We show [3] that certain kinds of lattice dislocations and bond defects in this system carry even more exotic excitations: unpaired Majorana fermions. Each pair of such defects (known as twists [4]) gives rise to a non-local physical (complex) fermion mode made out of two Majorana (real) fermions connected by a $Z_2$ gauge string. Their interaction decays exponentially with the distance. The non-local fermion can be created or annihilated by winding a vortex around a dislocation. The vortex also changes its topological charge in this process. The model remains exactly solvable in the presence of such defects and reveals a crucial role of the emergent gauge field in the physics of Majorana modes. \\[4pt] [1] A. Kitaev, Ann. Phys. \textbf{321}, 2 (2006). \\[0pt] [2] A. J. Willans, J. T. Chalker, and R. Moessner, Phys. Rev. B \textbf{84}, 115146 (2011). \\[0pt] [3] O. Petrova, P. Mellado, and O. Tchernyshyov, Phys. Rev. B \textbf{88}, 140405 (2013). \\[0pt] [4] H. Bombin, Phys. Rev. Lett. \textbf{105}, 030403 (2010).