  We analyze the Physics of cold atoms in honeycomb optical lattices with
on-site repulsion and spin-orbit couplings that break time reversal symmetry.
Such systems, at half filling and large on-site repulsion, have been proposed
as a possible realization of the Kitaev model. The spin-orbit couplings break
the spin degeneracy and, if strong-enough, lead to four non-overlapping bands
in the non-interacting limit. These bands carry non-zero Chern number and
therefore the non-interacting system has non-zero angular momentum and chiral
edge states at 1/4 and 3/4 filling. We have investigated the effect of
interactions using the variational cluster perturbation theory and conclude
that the chiral edge states exist in finite range of interaction and hopping
parameter space.
