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First order phase transitions in optical lattices with tunable three-body onsite interaction

We study the two-dimensional Bose-Hubbard model in the presence of a three-body interaction term, both at a mean field level and via quantum Monte Carlo simulations. The three-body term is tuned by coupling the triply occupied states to a trapped universal trimer. We find that, for sufficiently attractive three-body interaction the n = 2 Mott lobe disappears and the system displays first order phase transitions separating the n = 1 from the n = 3 lobes, and the n = 1 and n = 3 Mott insulator from the superfluid. We have also analyzed the effect of finite temperature and found that transitions are still of first order at temperatures T\simJ where J is the hopping matrix element.