Zero-Point Vacancies in Quantum Solids

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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 xv. We outline a route for estimating xv 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 xv 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, xv=(1.4±0.1)×10−6. For SWF, which presently gives the best variational energy of solid 4He, we find the significantly larger value xv=(1.4±0.1)×10−3 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.

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