Theory of the reentrant quantum rotational phase transition in high-pressure HD

The phase diagram of HD near 50 GPa exhibits a reentrant phase transition where a rotationally ordered (broken symmetry) crystalline phase surprisingly transforms into a rotationally disordered high-symmetry phase upon cooling. The qualitative reason for reentrance is the higher entropy of the broken symmetry phase, due to the inequivalence of H and D, as opposed to the low entropy of the high-symmetry phase where the rotational melting is quantum mechanical-a Pomeranchuk-like mechanism. Aiming at a quantitative understanding of this system, we present path integral Monte Carlo (MC) constant-pressure calculations for HD based on empirical but very realistic intermolecular interactions. Ignoring quantum mechanics at first, we use a metadynamics-based classical MC method to seek the lowest-energy zero-temperature classical state, which we identify as a very similar hcp-based structure C2/c as hypothesized by Surh et al. [Phys. Rev. B 55, 11330 (1997)]. Upon turning quantum rotational effects on, we calculate the pressure-temperature phase diagram by monitoring a lattice biased order parameter, and find a reentrant phase boundary in good agreement with experiment. The entropy jump across the transition is found to be comparable with ln 2, the value expected for a Pomeranchuk mechanism. A comparison with earlier studies is also presented, yielding relevant information about the role of factors that quantitatively determine the reentrant part of the phase diagram.