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

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

2011-11-14

arxiv.org/abs/1111.3296v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 6 figures

Scientific paper

We provide a microscopic understanding of the nucleation of topological quantum liquids for interacting non-Abelian anyons by making an explicit connection between the microscopics of the pairwise interactions -- typically showing RKKY-type behavior oscillating in sign, but decaying exponentially with distance -- and the nature of the collective many-anyon state. We investigate this issue 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 vortex-spacing or the strength of the time-reversal symmetry breaking field. By reformulating the interacting vortex superlattice in terms of an effective model of Majorana fermion zero modes, we show that the collective behavior can be fully traced back to the pairwise vortex interactions. We find that longer-range interactions beyond nearest neighbor can influence the nature of the collective state and thus need to be included for a comprehensive picture. Corresponding results should hold for vortices forming an Abrikosov lattice in a p-wave superconductor or quasiholes forming a Wigner crystal in non-Abelian quantum Hall states.

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