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

TL;DR

This study uses Path Integral Monte Carlo to estimate the onset temperature of Bose-Einstein condensation in incommensurate solid helium-4, revealing dependence on vacancy concentration and delocalization of vacancies below T_0.

Contribution

It provides the first computational estimate of the onset temperature of Bose-Einstein condensation in solid helium-4 with vacancies, showing non-trivial vacancy behavior.

Findings

T_0 depends on vacancy concentration X_v

T_0 does not follow the non-interacting vacancy law

Vacancies become delocalized below T_0

Abstract

The temperature dependence of the one-body density matrix in 4He crystals presenting vacancies is computed with Path Integral Monte Carlo. 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 $T_0 \sim X_v^{2/3}$ obtained assuming non-interacting vacancies. For the lowest X_v we have studied, that is X_v = 1/256, we get T_0 = (0.15 \pm 0.05) K, close to the temperatures at which a finite fraction of non-classical rotational inertia is experimentally observed. Below T_0, vacancies do not act as classical point defects becoming completely delocalized entities.