Supersolid hardcore bosons on the triangular lattice

We determine the phase diagram of hardcore bosons on a triangular lattice with nearest neighbor repulsion, paying special attention to the stability of the supersolid phase. Similar to the same model on a square lattice we find that for densities $\rho2/3$ a supersolid phase is unstable and the transition between a commensurate solid and the superfluid is of first order. At intermediate fillings $1/3 < \rho < 2/3$ we find an extended supersolid phase even at half filling $\rho=1/2$.