Quantum phase transitions in the attractive extended Bose-Hubbard model with a three-body constraint

The effect of nearest-neighbor repulsion on the ground-state phase diagrams of three-body constrained attractive Bose lattice gases is explored numerically. When the repulsion is turned on, in addition to the uniform Mott insulating state and two superfluid phases (the atomic and the dimer superfluids), a dimer checkerboard solid state appears at unit filling, where boson pairs form a solid with checkerboard structure. We find also that the first-order transitions between the uniform Mott insulating state and the atomic superfluid state can be turned into the continuous ones as the repulsion is increased. Moreover, the stability regions of the dimer superfluid phase can be extended to modest values of the hopping parameter by tuning the strength of the repulsion. Our conclusions hence shed light on the search of the dimer superfluid phase in real ultracold Bose gases in optical lattices.