  We consider a minimal model to describe the quantum phases of ultracold
dipolar bosons in two-dimensional (2D) 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 $0^{\circ}\leqslant\theta\apprle25^{\circ}$, the
ground state of the system are phases with checkerboard order, which could be
either checkerboard supersolid or checkerboard density wave. For high tilt
angles $55^{\circ}\apprge\theta\apprge35^{\circ}$, phases with striped order of
supersolid or density wave are preferred. In the intermediate domain
$25^{\circ}\apprle\theta\apprle35^{\circ}$ an emulsion or SF phase intervenes
the transition between the checkerboard and striped phases. The attractive
interaction dominates for $\theta\apprge55^{\circ}$, 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.
