Supersolid phases in the extended boson hubbard model

We present a comprehensive numerical study on the ground state phase diagram of the two-dimensional hardcore boson extended Hubbard model with nearest ($V_1$) and next nearest neighbor ($V_2$) repulsions. In addition to the quantum solid and superfluid phases, we report the existence of striped supersolid and three-quarter (quarter) filled supersolid at commensurate density $\rho =0.75$ (0.25) due to the interplay of $V_1$ and $V_2$ interactions. The nature of three-quarter filled supersolid and the associated quantum solid will be discussed. Quantum phase transition between the two supersolids of different symmetries is observed and is clearly of first order.