Supersolid Hard-Core Bosons on the Triangular Lattice

We determine the phase diagram of hard-core 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 $\rho <1/3$ or $\rho >2/3$ 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 $\rho =1/2$. The emergence of the supersolid on the triangular lattice reflects a novel and interesting way for a quantum system to avoid classical frustration, similar to an order-by-disorder mechanism. It also offers an exciting possibility of realizing such phenomena in ultracold atoms on optical lattices.