Off-Diagonal Long-Range Order in Solid 4He

We have found the first microscopic evidence for Bose-Einstein condensation (BEC) in crystalline 4He based on a quantitative variational theory of solid 4He: the shadow wave function technique. By computing the one-body density matrix 1 in solid 4He at T = 0 K, we find that off-diagonal long-range order is present for a perfect solid 4He for a range of densities above the melting one, at least up to 54 bars. The key process giving rise to BEC is the formation of vacancy-interstitial pairs (VIPs). Such processes have a finite probability to be present in the ground state of the system, and we have confirmed this also by an exact calculation. Due to exchange or other processes these VIPs are unbound; however they are not permanent excitations but simply fluctuations of the perfect crystal induced by the large zero-point motion