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