Supersolids versus Phase Separation in Two-Dimensional Lattice Bosons

We study the nature of the ground state of the two-dimensional extended boson Hubbard model on a square lattice by quantum Monte Carlo methods. We demonstrate that strong but finite on-site interaction $U$ along with a comparable nearest-neighbor repulsion $V$ result in a thermodynamically stable supersolid ground state for densities larger than $1/2$, in contrast to fillings less than $1/2$ or for very large $U$, where the checkerboard supersolid is unstable towards phase separation. We discuss the relevance of our results to realizations of supersolids using cold bosonic atoms in optical lattices.