Study of solid 4He in two dimensions : the issue of zero-point defects and study of confined crystal

Defects are believed to play a fundamental role in the supersolid state of 4 He. We report on studies by exact Quantum Monte Carlo (QMC) simulations at zero temperature of the properties of solid 4 He in presence of many vacancies, up to 30 in two dimensions (2D). In all studied cases the crystalline order is stable at least as long as the concentration of vacancies is below 2.5 %. In the 2D system for a small number, n v , of vacancies such defects can be identified in the crystalline lattice and are strongly correlated with an attractive interaction. On the contrary when n v 7310 vacancies in the relaxed system disappear and in their place one finds dislocations and a revival of the Bose-Einstein condensation. Thus, should zero-point motion defects be present in solid 4 He, such defects would be dislocations and not vacancies, at least in 2D. In order to avoid using periodic boundary conditions we have studied the exact ground state of solid 4 He confined in a circular region by an external potential. We find that defects tend to be localized in an interfacial region of width of about 15 \uc5. Our computation allows to put as upper bound limit to zero-point defects the concentration 3 710 123 in the 2D system close to melting density