We study the zero-temperature quantum phase transition between liquid and hcp solid helium-4. We use the variational method with a simple yet exchange-symmetric and fully explicit wavefunction. It is found that the optimized wavefunction undergoes sp
ontaneous symmetry breaking and describes the quantum solidification of helium at 22 atm. The explicit form of the wavefunction allows to consider various contributions to the phase transition. We find that the employed wavefunction is an excellent candidate for describing both a first-order quantum phase transition and the ground state of a Bose solid.
Equation of state of He-4 hcp crystals with vacancies is determined at zero temperature using the diffusion Monte Carlo technique, an exact ground state zero-temperature method. This allows us to extract the formation enthalpy and isobaric formation
energy of a single vacancy in otherwise perfect helium solid. Results were obtained for pressures up to 160 bar. The isobaric formation energy is found to reach a minimum near 57 bar where it is equal to $10.5pm 1.2$ K. At the same pressure, the vacancy formation volume exhibits a maximum and reaches the volume of the unit cell. This pressure coincides with the pressure interval over which a peak in the supersolid fraction of He-4 was observed in a recent experiment.
