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. 
Arghavan Safavi-Naini, Javier von Stecher, Barbara Capogrosso-Sansone,   Seth T. Rittenhouse
cond-mat.quant-gas cond-mat.stat-mech quant-ph