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

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