Off-Diagonal Long-Range Order in Solid ${}^4\mathrm{He}$

Measurements of the moment of inertia by Kim and Chan have found that solid ${}^4\mathrm{He}$ acts like a supersolid at low temperatures. To understand the order in solid ${}^4\mathrm{He}$, we have used path integral Monte Carlo simulations to calculate the off-diagonal long-range order (ODLRO) [equivalent to Bose-Einstein condensation (BEC)]. We do not find ODLRO in a defect-free hcp crystal of ${}^4\mathrm{He}$ at the melting density. We discuss these results in relation to proposed quantum solid trial functions. We conclude that the solid ${}^4\mathrm{He}$ wave function has correlations which suppress both vacancies and BEC.

Figure 1

The single particle density matrix as a function of distance (in Å), estimated with PIMC, in hcp ${}^4\mathrm{He}$ at a density $286{\mathrm{nm}}^{-3}$ and a temperature of 0.5 K. The solid (red) curve is the spherically averaged $n(r)$ while the dot-dashed (blue) curve is $n(x)$. The upper double-dot-dashed (green) curve is a variational MC calculation using the shadow wave function Ref. 25. The dashed straight line (black) has a slope determined from the exchange calculations of Ref. 5.