RPA approach to supersolidity

We investigate the newly discovered supersolid phase by solving in random phase approximation the anisotropic Heisenberg model of the hard-core boson ⁴He lattice. We include nearest- and next-nearest-neighbor interactions and calculate exactly all pair correlation functions in a cumulant expansion scheme. Here we clarify the controversy over the role of the vacancies and defects, which have long been proposed to have a crucial role in the formation of a SS phase. We show that vacancies and interstitials will be present even at zero temperature in the supersolid phase. This phase is characterized by Bose condensation of the vacancies as well as the interstitials and may be regarded as a bond-ordered wave as it exhibits alternating strength of the expectation value of the kinetic energy term on bonds. We also show that the superfluid-to-supersolid transition is triggered by a collapsing roton minimum, however, the supersolid phase is stable against spontaneously induced superflow.