  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.
