  We study the quantum ground state of ultracold bosons in a two-dimensional
square lattice. The bosons interact via the repulsive dipolar interactions and
s-wave scattering. The dynamics is described by the extended Bose-Hubbard model
including correlated hopping due to the dipolar interactions, the coefficients
are found from the second quantized Hamiltonian using the Wannier expansion
with realistic parameters. We determine the phase diagram using the Gutzwiller
ansatz in the regime where the coefficients of the correlated hopping terms are
negative and can interfere with the tunneling due to single-particle effects.
We show that this interference gives rise to staggered superfluid and
supersolid phases at vanishing kinetic energy, while we identify parameter
regions at finite kinetic energy where the phases are incompressible. We
compare the results with the phase diagram obtained with the cluster Gutzwiller
approach and with the results found in one dimension using DMRG.
