First-principles modeling of three-body interactions in highly compressed solid helium

TL;DR

This paper develops improved three-body interaction models for solid helium using ab initio calculations, accurately predicting its properties up to high pressures and highlighting the importance of many-body effects.

Contribution

The authors introduce new three-body potentials based on ab initio data that better reproduce experimental properties of solid helium under high pressure.

Findings

Accurately reproduce the equation of state and bulk modulus up to 60 GPa.

Show that previous predictions of constant kinetic energy are artifacts of incomplete models.

Quantitatively describe the shear modulus variation at pressures below 25 GPa.

Abstract

We present a new set of three-body interaction models based on the Bruch-McGee (BM) potential that are suitable for the study of the energy, structural and elastic properties of solid 4He at high pressure. Our ab initio three-body potentials are obtained from the fit to total energies and atomic forces computed with the van der Waals density functional theory method due to Grimme, and represent an improvement with respect to previously reported three-body interaction models. In particular, we show that some of the introduced BM parametrizations reproduce closely the experimental equation of state and bulk modulus of solid helium up to a pressure of ~ 60 GPa, when used in combination with standard pairwise interaction models in diffusion Monte Carlo simulations. Importantly, we find that recent predictions reporting a surprisingly small variation of the kinetic energy and Lindeman ratio on quantum crystals under increasing pressure are likely to be artifacts produced by the use of incomplete interaction models. Also, we show that the experimental variation of the shear modulus, C44, at P < 25 GPa can be quantitatively described with the new set of three-body BM potentials. At higher pressures, however, the agreement between our C44 results and experiments deteriorates and thus we argue that higher order many-body terms in the expansion of the atomic interactions probably are necessary in order to better describe elasticity in very dense solid 4He.