Superfluid-insulator transitions in attractive Bose-Hubbard model with three-body constraint

By means of the method of the effective potential, the phase transitions from the Mott insulating state to either the atomic or the dimer superfluid state in the three-body constrained attractive Bose lattice gas are analyzed. Because of the appearance of the Feshbach resonance coupling between the two kinds of order parameters in the derived Ginzburg-Landau function, it is found that the continuous Mott-insulator-superfluid transitions can be preempted by first-order ones. Since the employed approach can provide accurate predictions of phase boundaries in the strong coupling limit, where the dimer superfluid phase can emerge, our work sheds light on the search of this phase in real ultracold Bose gases in optical lattices.