  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.
