  We study the repulsive Hubbard model on an anisotropic honeycomb lattice
within a mean-field and a slave-rotor treatment. In addition to the known
semi-metallic and band-insulating phases, obtained for very weak interactions,
and the anti-ferromagnetic phase at large couplings, various insulating
spin-liquid phases develop at intermediate couplings. Whereas some of these
spin liquids have gapless spinon excitations, a gapped one occupies a large
region of the phase diagram and becomes the predominant phase for large hopping
anisotropies. This phase can be understood in terms of weakly-coupled strongly
dimerized states.
