Supersolids versus phase separation in two-dimensional lattice bosons
  We study the nature of the ground state of the strongly-coupled two dimensional extended boson Hubbard model on a square lattice. 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 just above half-filling, and that the checker-board crystal is unstable for smaller V, and for any V just below half-filling. The interplay between these two interaction energies results in a rich phase diagram which is studied in detail using quantum Monte Carlo methods. 
Pinaki Sengupta, Leonid P. Pryadko, Fabien Alet, Matthias Troyer,   Guido Schmid