Bose Einstein Condensation in solid 4He

TL;DR

This study provides the first microscopic evidence of Bose-Einstein Condensation in perfect solid 4He, showing off-diagonal long-range order and a small condensate fraction influenced by vacancy-interstitial pairs.

Contribution

It introduces a microscopic calculation demonstrating BEC in perfect solid 4He using the Shadow Wave Function method, validated against an exact projector technique.

Findings

Off-diagonal long-range order exists in solid 4He at zero temperature.

The condensate fraction is approximately 5×10^{-6} at melting density.

Vacancy-interstitial pairs are key to the emergence of BEC in solid helium.

Abstract

We have computed the one--body density matrix rho_1 in solid 4He at T=0 K using the Shadow Wave Function (SWF) variational technique. The accuracy of the SWF has been tested with an exact projector method. We find that off-diagonal long range order is present in rho_1 for a perfect hcp and bcc solid 4He for a range of densities above the melting one, at least up to 54 bars. This is the first microscopic indication that Bose Einstein Condensation (BEC) is present in perfect solid 4He. At melting the condensate fraction in the hcp solid is 5*10^{-6} and it decreases by increasing the density. The key process giving rise to BEC is the formation of vacancy--interstitial pairs. We also present values for Leggett's upper bound on the superfluid fraction deduced from the exact local density.