Vacancy supersolid of hard-core bosons on the square lattice

The ground state of hard-core bosons on the square lattice with nearest and next-nearest-neighbor repulsion is studied by quantum Monte Carlo simulations. A supersolid phase with vacancy condensation and "star" diagonal ordering is found for filling rho < 0.25. At filling rho>0.25, a supersolid phase exists between the star and the stripe crystal at rho=0.5. No supersolid phase occurs for rho>0.25 if the ground state at half-filling is either a checkerboard crystal or a superfluid. No commensurate supersolid phase is observed.