Quantum phases of canted dipolar bosons in a two-dimensional square optical lattice

We consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle theta of the dipolar bosons. At low tilt angles, 0 degrees <= theta less than or similar to 25 degrees, the ground states of the system are phases with checkerboard order, which can be either checkerboard supersolids or checkerboard density waves. For high tilt angles, 35 degrees less than or similar to theta less than or similar to 55 degrees, phases with striped order of the supersolid or density wave are preferred. In the intermediate domain, 25 degrees less than or similar to theta less than or similar to 35 degrees, an emulsion or superfluid phase intervenes the transition between the checkerboard and the striped phases. The attractive interaction dominates at theta greater than or similar to 55 degrees, which renders the system unstable, and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second-order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results. In our study, the incompressible phases have an average occupancy per site rho <= 1, but the compressible phases can have rho > 1.