  Recently, it has become apparent that, when the interactions between polar
molecules in optical lattices becomes strong, the conventional description
using the extended Hubbard model has to be modified by additional terms, in
particular a density-dependent tunneling term. We investigate here the
influence of this term on the ground-state phase diagrams of the two
dimensional extended Bose-Hubbard model. Using Quantum Monte Carlo simulations,
we investigate the changes of the superfluid, supersolid, and phase-separated
parameter regions in the phase diagram of the system. By studying the interplay
of the density-dependent hopping with the usual on-site interaction U and
nearest-neighbor repulsion V, we show that the ground-state phase diagrams
differ significantly from the ones that are expected from the standard extended
Bose-Hubbard model. However we find no indication of pair-superfluid behavior
in this two dimensional square lattice study in contrast to the one-dimensional
case.
