Antiferromagnetic Order and Bose-Einstein Condensation in Strongly-Correlated Cold-Atom Systems: Bosonic t-J Model in the Double-CP¹ Representation

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We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons" at finite temperatures. This model describes a system of cold bosonic atoms with two species in an optical lattice. The model is derived from the Hubbard model for very large on-site repulsive interaction between bosons of same species (hard-core nature) and also strong correlations between different species. The operator Bₓσ for an atom at the site x 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 CP¹ field (Schwinger boson) zₓσ and a holon described by a hard-core-boson field ϕₓ as Bₓσ=ϕ†ₓ zₓσ. ϕₓ is then expressed by a pseudo-spin, which is, in turn, represented by another CP¹ (pseudo) spinon wₓη as ϕₓ = wₓ₂†wₓ₁. We then have a double-CP¹ representation of the model by zₓσ and wₓη. By means of Monte Carlo simulations of this bosonic t-J model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. They should be compared with the possible experimental results of a recently studied boson-boson mixture like ⁸7Rb and ⁴1K in an optical lattice.