Supersolidity and phase diagram of soft-core bosons on a triangular lattice

We study the soft-core extended Bose-Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground-state phase diagram of the system exhibits a very fruitful structure and is much intriguing. Aside from the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors rho=1/3,2/3 and rho=1 are identified. In incommensurate fillings, superfluid, supersolid, as well as phase-separation states are detected. As in the case of the hard-core bosons, a supersolid phase exists in 1/3 <rho < 2/3 while it is unstable toward the phase separation in rho < 1/3. However, this instability is refrained in 2/3 <rho < 1 due to the softening of the bosons, and then a supersolid phase survives.