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Finite-temperature phase diagram of two-component bosons in a cubic optical lattice: Three-dimensional t-J model of hard-core bosons

We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons", at finite temperatures. This model describes the $s={1 \over 2}$ Heisenberg spin model with the anisotropic exchange coupling $J_{\bot}=-αJ_z$ and doped {\it bosonic} holes, which is an effective system of the Bose-Hubbard model with strong repulsions. The bosonic "electron" operator $B_{rσ}$ at the site $r$ with a two-component (pseudo-)spin $σ(=1,2)$ is treated as a hard-core boson operator, and represented by a composite of two slave particles; a "spinon" described by a Schwinger boson (CP$^1$ boson) $z_{rσ}$ and a "holon" described by a hard-core-boson field $ϕ_r$ as $B_{rσ}=ϕ^†_r z_{rσ}$. By means of Monte Carlo simulations, we study its finite-temperature phase structure including the $α$ dependence, the possible phenomena like appearance of checkerboard long-range order, super-counterflow, superfluid, and phase separation, etc. The obtained results may be taken as predictions about experiments of two-component cold bosonic atoms in the cubic optical lattice.