Speaker
Ville Lahtinen
(NORDITA)
Description
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. 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.
