Equation of state of metallic hydrogen from Coupled Electron-Ion Monte Carlo simulations

TL;DR

This study uses advanced Monte Carlo simulations to accurately determine the equation of state of metallic hydrogen at high pressures, validating some DFT results and challenging existing planetary models.

Contribution

First application of Coupled Electron-Ion Monte Carlo to metallic hydrogen, providing highly accurate EOS data and comparison with DFT and chemical models.

Findings

Good agreement with DFT for pressures >600 GPa

DFT accurately reproduces thermodynamic and structural properties

Disagreement with chemical models suggests need for re-evaluation of planetary models

Abstract

We present a study of hydrogen at pressures higher than molecular dissociation using the Coupled Electron-Ion Monte Carlo method. These calculations use the accurate Reptation Quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of phase space, we report the free energy obtained by thermodynamic integration. We find very good agreement with DFT calculations for pressures beyond 600 GPa and densities above $\rho=1.4 g/cm^3$. Both thermodynamic as well as structural properties are accurately reproduced by DFT calculations. This agreement gives a strong support to the different approximations employed in DFT, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests a reinvestigation of planetary models, previously constructed using the Saumon-Chabrier-Van Horn equations of state.