Abstract
A t–J1–J2 model is constructed to describe the spin-1 bosons in opticallattices in the strong correlation limit. In the parameter region ofJ1<J2, with the slave-boson-mean-field approach, it is found that two kinds of condensed phases mayexist: a condensate with spin singlet pairs and a condensate with ferro-quadruple long rangeorder coexisting with singlet pairs. A first-order quantum phase transition occurs at the pointJ1 = 0. The finite-temperature phase transition in a cubic optical lattice was also discussed.
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