  We study a two-dimensional bosonic Hubbard model with two hard-core species
away from half filling using Quantum Monte Carlo simulations. The model
includes a repulsive interspecies interaction and different nearest-neighbor
hopping terms for the two species. By varying the filling we find a total of
five distinct phases, including a normal liquid phase at higher temperature,
and four different phases at lower temperature. We find an
anti-ferromagnetically ordered Mott insulator and a region of coexistent
anti-ferromagnetic and superfluid phases near half filling. Further away from
half filling the phase diagram displays a superfluid phase and a novel phase
inside the superfluid region at even lower temperatures. In this novel phase
separated region, the heavy species has a Mott behavior with integer filling,
while the lighter species shows phase separated Mott and superfluid behaviors.
