  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 at zero temperature. We include nearest and next-nearest
neighbor interactions and calculate exactly all pair correlation functions in a
cumulant decoupling scheme. We demonstrate the importance of vacancies and
interstitials in the formation of the supersolid phase. The supersolid phase is
characterised by strong quantum fluctuations which are taken into account
rigorously. Furthermore we confirm that the superfluid to supersolid transition
is triggered by a collapsing roton minimum however is stable against
spontaneously induced superflow, i.e. vortex creation.
