Onset temperature of Bose-Einstein condensation in incommensurate solid (4)He

The temperature dependence of the one-body density matrix in (4)He crystals presenting vacancies is computed with path integral Monte Carlo simulations. The main purpose of this study is to estimate the onset temperature T(0) of Bose-Einstein condensation in these systems. We see that T(0) depends on the vacancy concentration X(v) of the simulated system, but not following the law T(0) ~ X(v)(2/3) obtained assuming noninteracting vacancies. For the lowest X(v) we study, that is X(v)= 1/256, we get T(0) = 0.15 ± 0.05 K, close to the temperatures at which a finite fraction of nonclassical rotational inertia is experimentally observed. Below T(0), vacancies do not act as classical point defects becoming completely delocalized entities.