Topological liquid nucleation induced by vortex-vortex interactions in Kitaev's honeycomb model

Ville Lahtinen, Andreas W. W. Ludwig, Jiannis K. Pachos, Simon Trebst

Published 2011-11-14, updated 2012-08-14Version 4

We provide a comprehensive microscopic understanding of the nucleation of topological quantum liquids, a general mechanism where interactions between non-Abelian anyons cause a transition to another topological phase, which we study in the context of Kitaev's honeycomb lattice model. For non-Abelian vortex excitations arranged on superlattices, we observe the nucleation of several distinct Abelian topological phases whose character is found to depend on microscopic parameters such as the superlattice spacing or the spin exchange couplings. By reformulating the interacting vortex superlattice in terms of an effective model of Majorana fermion zero modes, we show that the nature of the collective many-anyon state can be fully traced back to the microscopic pairwise vortex interactions. Due to RKKY-type sign oscillations in the interactions, we find that longer-range interactions beyond nearest neighbor can influence the collective state and thus need to be included for a comprehensive picture. The omnipresence of such interactions implies that corresponding results should hold for vortices forming an Abrikosov lattice in a p-wave superconductor, quasiholes forming a Wigner crystal in non-Abelian quantum Hall states or topological nanowires arranged in regular arrays.