Zero-temperature equation of state of solid 4He at low and high pressures

TL;DR

This study investigates the zero-temperature equation of state of solid 4He across a wide pressure range using diffusion Monte Carlo and density functional theory, achieving good agreement at low pressures and improved accuracy at high pressures with corrections.

Contribution

It combines DMC and DFT methods to accurately model the EOS of solid 4He over a broad pressure range, including corrections for many-body interactions at high pressures.

Findings

Excellent agreement with experiments at low pressures

Discrepancies reduced to 5-10% at high pressures with DFT corrections

EOS curves consistent with ab initio calculations including zero-point motion

Abstract

We study the zero-temperature equation of state (EOS) of solid 4He in the hexagonal closed packet (hcp) phase over the 0-57 GPa pressure range by means of the Diffusion Monte Carlo (DMC) method and the semi-empirical Aziz pair potential HFD-B(HE). In the low pressure regime (P ~ 0-1 GPa) we assess excellent agreement with experiments and we give an accurate description of the atomic kinetic energy, Lindemann ratio and Debye temperature over a wide range of molar volumes (22-6 cm^{3}/mol). However, on moving to higher pressures our calculated P-V curve presents an increasingly steeper slope which ultimately provides differences within ~40 % with respect to measurements. In order to account for many-body interactions arising in the crystal with compression which are not reproduced by our model, we perform additional electronic density-functional theory (DFT) calculations for correcting the computed DMC energies in a perturbative way. We explore both generalized gradient and local density approximations (GGA and LDA, respectively) for the electronic exchange-correlation potential. By proceeding in this manner, we show that discrepancies with respect to high pressure data are reduced to 5-10 % with few computational extra cost. Further comparison between our calculated EOSs and ab initio curves deduced for the perfect crystal and corrected for the zero-point motion of the atoms enforces the reliability of our approach.