Supersolid phase transitions for hardcore bosons on a triangular lattice
  Hard-core bosons on a triangular lattice with nearest neighbor repulsion are a prototypical example of a system with supersolid behavior on a lattice. We show that in this model the physical origin of the supersolid phase can be understood quantitatively and analytically by constructing quasiparticle excitations of defects that are moving on an ordered background. The location of the solid to supersolid phase transition line is predicted from the effective model for both positive and negative (frustrated) hopping parameters. For positive hopping parameters the calculations agree very accurately with numerical Quantum Monte Carlo simulations. The numerical results indicate that the supersolid to superfluid transition is first order. 
Xue-Feng Zhang, Raoul Dillenschneider, Yue Yu, and Sebastian Eggert
cond-mat.quant-gas cond-mat.str-el quant-ph