Quantum phase transitions from Solids to Supersolids in bi-partite lattices

We studied some phases and phase transitions in an extended boson Hubbard model slightly away from half filling on bipartite lattices such as honeycomb and square lattice. We find that in the insulating side, different kinds of supersolids are generic stable states slightly away from half filling. We propose a new kind of supersolid: valence bond supersolid. We show that the quantum phase transitions from solids to supersolids driven by a chemical potential are in the same universality class as that from a Mott insulator to a superfluid, therefore have exact exponents $ z=2, \nu=1/2, \eta=0 $ (with logarithmic corrections). Comparisons with previous quantum Monte-Carlo (QMC) simulations on some microscopic models on a square lattice are made. Implications on possible future QMC simulations are given.