The bosonic t-J model is a strong-on-site repulsion limit of the two-component Bose-Hubbard model and is expected to be realized by experiments of cold atoms in an optical lattice. In previous papers, we studied the bosonic t-J model by both analytical methods and numerical Monte - Carlo (MC) simulations. However, in the case of finite
Jz, where
Jz is the
z-component coupling constant of the pseudospin interaction, the phase diagram of the model was investigated by assuming the checkerboard type of boson densities. In this study, we shall continue our previous study of the bosonic t-J model using both the Gross-Pitaevskii (GP) theory and MC simulations without assuming any pattern of boson densities. These two methods complement each other and give reliable results. We show that as
Jz is increased, the superfluid state evolves into a supersolid (SS), and furthermore into a genuine solid with the checkerboard symmetry. In the present study, we propose a method identifying quantum phase transitions in the GP theory. We also study finite-temperature phase transitions of the superfluidity and the diagonal solid order of the SS by MC simulations.
We perform a stability analysis of superfluid (SF) and supersolid (SS) phases of polarized dipolar bosons in two-dimensional optical lattices at high filling factors and zero temperature, and obtain the phase boundaries between SF, checkerboard SS (CSS), striped SS (SSS), and collapse. We show that the phase diagram can be explored through the application of an external field and the tuning of its direction with respect to the optical lattice plane. In particular, we find a transition between the CSS and SSS phases.