Solids and supersolids of three-body interacting polar molecules in an optical lattice

We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by B\"uchler [Nature Phys. 3, 726 (2007)]. To this end quantum Monte Carlo simulations, exact diagonalization and a semiclassical approach are used to explore hardcore bosons on the two-dimensional square lattice which interact solely by long ranged three-body terms. The resulting phase diagram shows a sequence of solid and supersolid phases. Our findings are directly relevant for future experimental implementations and open a new route towards the discovery of a lattice supersolid phase in experiment.