  We investigate the newly discovered supersolid phase by solving in random
phase approximation the anisotropic Heisenberg model of the hard-core boson
${}^4$He lattice. We include nearest and next-nearest neighbor interactions and
calculate exactly all pair correlation functions in a cumulant expansion
scheme. We describe the properties of the normal solid and supersolid phases
and argue that based on analogies to the fermionic half filled extended Hubbard
model the supersolid state corresponds to a bond-ordered-wave.
