Recent progress in simulation of the ground state of many Boson systems

We present two recent advances in the simulation of He-4 in the condensed phase at zero temperature. Within the variational theory of strongly interacting bosons we have studied a cluster of He-4 atoms with one alkali ion K+. For the wave function we have used a new shadow wave function (SWF) in which the coupling between one He-4 atom and its shadow variable depends on its distance from the ion. This substantially improves the energy. The first shell around the ion contains 14 atoms which are spatially ordered. However the atoms of the first shell are not completely localized and frequent exchanges with atoms which are further from the ion take place. This also suggests that at least for the ion K+ the atoms of the first shell participate in the superfluidity. We have also introduced a new extension of the path integral ground state (PIGS) method which is able to compute exact ground state expectation values without extrapolations and with a SWF as the trial variational wave function to project on the ground state. This is an important extension which opens up the possibility of studying disorder phenomena in the solid phase by an exact method at zero temperature. We have applied this technique to compute the energy of formation of a vacancy at different densities in the solid phase of He-4. This computation confirms the variational result that a vacancy is a delocalized defect in the low density helium solid.