Zero-point vacancies in quantum solids

Details Zero-point vacancies in quantum solids Zero-point vacancies in quantum solids

2008-06-13

arxiv.org/abs/0806.2225v1

J. Low Temp. Phys. 153 (2008) : 250-265

Physics

Condensed Matter

Other Condensed Matter

19 pages, submitted to J. Low Temp. Phys

Scientific paper

10.1007/s10909-008-9830-6

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\pm0.1) x 10^-6. For SWF, which presently gives the best variational description of solid 4He, we find the significantly larger value x_v=(1.4\pm0.1) x 10^-3 at a density close to melting. We also study two and three vacancies. We find that there is a strong short range attraction but the vacancies do not form a bound state.

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