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In this paper, we study an extended bosonic t-J model in an optical lattice,which describes two-component hard-core bosons with a nearest-neighbor (NN)pseudo-spin interaction, and also inter- and intra-species dipole-dipoleinteractions (DDI). In particular, we focus on the case in which two componenthard-core bosons have anti-parallel polarized dipoles with each other. Theglobal phase diagram is studied by means of the Gutzwiller variational methodand also the quantum Monte-Carlo simulations (QMC). The both calculations showthat a stripe solid order, besides a checkerboard one, appears as a result ofthe DDI. By the QMC, we find that two kinds of supersolid (SS) form,checkerboard SS and stripe SS, and we also verify the existence of some exoticphase between the stripe solid and checkerboard SS. Finally by the QMC, westudy the t-J-like model, which was experimentally realized recently by A. dePaz et al. [Phys. Rev. Lett. {\bf 111}, 185305 (2013)].

Superfluidity and solid orders in two-component Bose gas with dipolar interactions in an optical lattice