  In the present paper, we study finite-temperature phase structure of
two-component hard-core bosons in a cubic optical lattice. The system that we
study in the present paper is an effective model for the Bose-Hubbard model
with strong on-site repulsions and is called bosonic t-J model. This model is a
bosonic counterpart of the t-J model for the strongly-correlated electron
systems like the high-temperature superconducting materials. We study the model
by means of path-integral methods and Monte-Carlo simulations. We found that
this system has a very rich phase structure including checkerboard-type
"insulating" state, superfluid, phase-separated state, inhomogeneous cloudlet
state, etc. We are also interested in the possible supersolid phase with both
the checkerboard order and superfluidity and found that additional
nearest-neighbor inter-species attractive force induces the supersolid state.
In the supersolid state, paired superfluid appears in addition to the
superfluid of single atom. This result gives important insight into mechanism
of the high-temperature superconductivity of the cuprate.
