Zero-temperature study of vacancies in solid 4 He

We are investigating the properties of vacancies in solid 4 He with the exact zero temperature SPIGS method. Our aim is to study the possibility of phase-separation between vacancies and the perfect crystal. We find a significant correlation among vacancies both in two and in three dimensional solid He. In 3 D we have considered up to 5 vacancies in a hcp crystal at a density ρ = 0.0293Å -3 , close to the melting, and in 2D we have considered up to 6 vacancies in a triangular crystal at ρ = 0.0765Å -2 . In all the considered cases the correlation among vacancies seems to display an exponential decay that would suggest the presence of a bound state. The systematically sublinear dependence on the number of vacancies found for the activation energy strengthens the indication of an attractive interaction, even if we have direct evidence that vacancies do not form a single compact cluster.