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

Quarter-filled Kitaev-Hubbard Model: A Quantum Hall State in an Optical Lattice