Off-Diagonal Long-Range Order in SolidHe4

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.