Zero-point vacancies in quantum solids

TL;DR

This paper estimates zero-point vacancy concentrations in quantum solids using wave functions, revealing extremely low vacancy levels for Jastrow and higher for shadow wave functions, with implications for supersolidity.

Contribution

It introduces a method to estimate vacancy concentrations in quantum solids from wave function formalism and provides numerical estimates for Jastrow and shadow wave functions.

Findings

Jastrow wave function predicts vacancy concentration ~10^-6

Shadow wave function predicts vacancy concentration ~10^-3

Vacancies exhibit strong short-range attraction but do not form bound states

Abstract

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.