  The Lennard-Jones potential is perhaps one of the most widely-used models for
the interaction of uncharged particles, such as noble gas solids. The phase
diagram of the classical LJ solid is known to exhibit transitions between hcp
and fcc phases. However, the phase behaviour of the quantum Lennard-Jones solid
remains unknown. Thermodynamic integration based on path integral molecular
dynamics and lattice dynamics calculations are used to study the phase
stability of the hcp and fcc Lennard-Jones solids. The hcp phase is shown to be
stabilized by quantum effects in PIMD while fcc is shown to be favoured by
lattice dynamics, which suggests a possible re-entrant low pressure hcp phase
for highly quantum systems. Implications for the phase stability of noble gas
solids are discussed. For parameters equating to Helium, the expansion due to
zero-point vibrations is associated with quantum melting: neither crystal
structure is stable at zero pressure.
