  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.
