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High-finesse optical cavity allows the establishment of long-rangeinteractions between bosons in an optical lattice when most cold atomsexperiments are restricted to short-range interactions. Supersolid phases haverecently been experimentally observed in such systems. Using both exact quantumMonte Carlo simulations and Gutzwiller approximation, we study the ground statephase diagrams of a two-dimensional Bose-Hubbard model with infinite-rangeinteractions which describes such experiments. In addition to superfluid andinsulating Mott phases, the infinite-range checkerboard interactions introducecharge density waves and supersolid phases. We study here the system at variousparticle densities, elucidate the nature of the phases and quantum phasetransitions, and discuss the stability of the phases with respect to phaseseparation. In particular we confirm the existence and stability of asupersolid phase detected experimentally.

Phase Diagram of Bosons in a 2D Optical Lattice with infinite-range Cavity-mediated Interactions