Finite Temperature Properties of a Supersolid: a RPA Approach

We study in random-phase approximation the newly discovered supersolid phase of ${}^4$He and present in detail its finite temperature properties. ${}^4$He is described within a hard-core quantum lattice gas model, with nearest and next-nearest neighbour interactions taken into account. We rigorously calculate all pair correlation functions in a cumulant decoupling scheme. Our results support the importance of the vacancies in the supersolid phase. We show that in a supersolid the net vacancy density remains constant as function of temperature, contrary to the thermal activation theory. We also analyzed in detail the thermodynamic properties of a supersolid, calculated the jump in the specific heat which compares well to the recent experiments.