  The spectral properties of Kitaev's honeycomb lattice model are investigated
both analytically and numerically with the focus on the non-abelian phase of
the model. After summarizing the fermionization technique which maps spins into
free Majorana fermions, we evaluate the spectrum of sparse vortex
configurations and derive the interaction between two vortices as a function of
their separation. We consider the effect vortices can have on the fermionic
spectrum as well as on the phase transition between the abelian and non-abelian
phases. We explicitly demonstrate the $2^n$-fold ground state degeneracy in the
presence of $2n$ well separated vortices and the lifting of the degeneracy due
to their short-range interactions. The calculations are performed on an
infinite lattice. In addition to the analytic treatment, a numerical study of
finite size systems is performed which is in exact agreement with the
theoretical considerations. The general spectral properties of the non-abelian
phase are considered for various finite toroidal systems.
