3 research outputs found
Interacting non-Abelian anyons as Majorana fermions in the honeycomb lattice model
We study the collective states of interacting non-Abelian anyons that emerge
in Kitaev's honeycomb lattice model. Vortex-vortex interactions are shown to
lead to the lifting of the topological degeneracy and the energy is discovered
to exhibit oscillations that are consistent with Majorana fermions being
localized at vortex cores. We show how to construct states corresponding to the
fusion channel degrees of freedom and obtain the energy gaps characterizing the
stability of the topological low energy spectrum. To study the collective
behavior of many vortices, we introduce an effective lattice model of Majorana
fermions. We find necessary conditions for it to approximate the spectrum of
the honeycomb lattice model and show that bi-partite interactions are
responsible for the degeneracy lifting also in many vortex systems.Comment: 22 pages, 12 figures, published versio