The uniform electron gas at high temperatures: \emph{ab initio} path integral Monte Carlo simulations and analytical theory

TL;DR

This paper provides extensive ab initio path integral Monte Carlo simulations and analytical insights into the high-temperature behavior of the uniform electron gas, exploring properties like structure factors, interaction energy, and momentum distribution.

Contribution

It offers new high-temperature PIMC data and analytical comparisons for the uniform electron gas, extending understanding and benchmarking for this fundamental model.

Findings

Classical relation between structure factor and local field correction holds only at low densities.

Interaction energy results align with existing parametrizations and virial expansions.

Zero-momentum state occupation increases due to interactions even at high temperatures.

Abstract

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of the uniform electron gas (UEG) in the high-temperature regime, $8\leq\theta=k_\textnormal{B}T/E_\textnormal{F}\leq128$. This allows us to study the convergence of different properties towards the classical limit. In particular, we investigate the classical relation between the static structure factor $S(\mathbf{q})$ and the static local field correction $G(\mathbf{q})$, which is only fulfilled at low densities. Moreover, we compare our new results for the interaction energy to the parametrization of the UEG by Groth \emph{et al.}~[PRL \textbf{119}, 135001 (2017)], which interpolates between PIMC results for $\theta\leq8$ and the Debye-H\"uckel limit, and to higher order analytical virial expansions. Finally, we consider the momentum distribution function $n(\mathbf{q})$ and find an interaction-induced increase in the occupation of the zero-momentum state even for $\theta\gtrsim32$. All PIMC data are freely available online, and can be used as input for improved parametrizations and as a rigorous benchmark for approximate methods.