Quantum Phases of Cold Polar Molecules in 2D Optical Lattices

We discuss the quantum phases of hard-core bosons on a two-dimensional square lattice interacting via repulsive dipole-dipole interactions, as realizable with polar molecules trapped in optical lattices. In the limit of small tunneling, we find evidence for a devil's staircase, where solid phases appear at all rational fillings of the underlying lattice. For finite tunneling, we establish the existence of extended regions of parameters where the groundstate is a supersolid, obtained by doping the solids either with particles or vacancies. Here the solid-superfluid quantum melting transition consists of two consecutive second-order transitions, with a supersolid as the intermediate phase. The effects of finite temperature and confining potentials relevant to experiments are discussed.