  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. Due to the
appearance of the Feshbach resonance coupling between the two kinds of order
parameters in the derived effective potential function, it is found that the
continuous Mott insulator-to-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 hence sheds light on the search of this novel phase
in real ultracold Bose gases in optical lattices.
