Accurate exchange-correlation energies for the warm dense electron gas

TL;DR

This paper uses density matrix quantum Monte Carlo to accurately compute exchange-correlation energies of the warm dense electron gas, resolving discrepancies between different methods and providing reliable data for planetary and solid-state conditions.

Contribution

It introduces the application of DMQMC to calculate exact free energies and resolve accuracy debates in finite-temperature density functional data.

Findings

DMQMC samples large density matrices for electron gases.

Discrepancies between real-space and k-space path-integral results are up to 10%.

Provides trustworthy data for planetary and solid-state regimes.

Abstract

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the $k$-space configuration path-integral formalism disagree by up to $\sim$$10$\% at certain reduced temperatures $T/T_F \le 0.5$ and densities $r_s \le 1$. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that DMQMC can calculate free energies directly and present exact free energies for $T/T_F \ge 1$ and $r_s \le 2$.