Onset Temperature of Bose-Einstein Condensation in Incommensurate Solid 4He

The temperature dependence of the one-body density matrix in He-4 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 similar to X-v(2/3) v obtained assuming noninteracting vacancies. For the lowest Xv 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.