Zero-point vacancies in quantum solids

A Jastrow wave function (JWF) and a shadow wave function (SWF) describe a quantum solid with Bose-Einstein condensate; i.e. a supersolid. It is known that both JWF and SWF describe a quantum solid with also a finite equilibrium concentration of vacancies x (v) . We outline a route for estimating x (v) by exploiting the existing formal equivalence between the absolute square of the ground state wave function and the Boltzmann weight of a classical solid. We compute x (v) for the quantum solids described by JWF and SWF employing very accurate numerical techniques. For JWF we find a very small value for the zero point vacancy concentration, x (v) =(1.4 +/- 0.1)x10-6. For SWF, which presently gives the best variational energy of solid 4He, we find the significantly larger value x (v) =(1.4 +/- 0.1)x10-3 at a density close to melting. We also study two and three vacancies with SWF. We find that there is a strong short range attraction but the vacancies do not form a bound state, at variance with the exact finite temperature PIMC results.