{\em Ab initio} Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit

TL;DR

This paper presents highly accurate ab initio quantum Monte Carlo simulations of the warm dense electron gas, effectively removing finite-size errors and providing new benchmark data for potential energy and exchange-correlation free energy.

Contribution

The study introduces a novel combination of QMC data with linear response theory to eliminate finite-size errors in warm dense electron gas simulations, surpassing previous correction methods.

Findings

Achieved potential energy and free energy calculations with ~0.1% accuracy.

Provided extensive new QMC data for systems with up to 1000 electrons.

Identified significant deviations from existing parametrizations of exchange-correlation free energy.

Abstract

We perform \emph{ab initio} quantum Monte Carlo (QMC) simulations of the warm dense uniform electron gas in the thermodynamic limit. By combining QMC data with linear response theory we are able to remove finite-size errors from the potential energy over the entire warm dense regime, overcoming the deficiencies of the existing finite-size corrections by Brown \emph{et al.}~[PRL \textbf{110}, 146405 (2013)]. Extensive new QMC results for up to $N=1000$ electrons enable us to compute the potential energy $V$ and the exchange-correlation free energy $F_{xc}$ of the macroscopic electron gas with an unprecedented accuracy of $|\Delta V|/|V|, |\Delta F_{xc}|/|F|_{xc} \sim 10^{-3}$. A comparison of our new data to the recent parametrization of $F_{xc}$ by Karasiev {\em et al.} [PRL {\bf 112}, 076403 (2014)] reveals significant deviations to the latter.