Permutation blocking path integral Monte Carlo approach to the uniform electron gas at finite temperature

TL;DR

This paper introduces an extension of the permutation blocking path integral Monte Carlo method to study the uniform electron gas at finite temperature, providing new data that aligns with some methods and deviates from others at high densities.

Contribution

The authors develop and apply a permutation blocking path integral Monte Carlo approach to the uniform electron gas, covering a wide density range and offering independent validation of existing methods.

Findings

Excellent agreement with CPIMC results.

Deviations from RPIMC increase with density.

Method effective down to half the Fermi temperature.

Abstract

The uniform electron gas (UEG) at finite temperature is of high current interest due to its key relevance for many applications including dense plasmas and laser excited solids. In particular, density functional theory heavily relies on accurate thermodynamic data for the UEG. Until recently, the only existing first-principle results had been obtained for $N=33$ electrons with restricted path integral Monte Carlo (RPIMC), for low to moderate density, $r_s = \overline{r}/a_B \gtrsim 1$. This data has been complemented by Configuration path integral Monte Carlo (CPIMC) simulations for $r_s \leq 1$ that substantially deviate from RPIMC towards smaller $r_s$ and low temperature. In this work, we present results from an independent third method---the recently developed permutation blocking path integral Monte Carlo (PB-PIMC) approach [T. Dornheim \textit{et al.}, NJP \textbf{17}, 073017 (2015)] which we extend to the UEG. Interestingly, PB-PIMC allows us to perform simulations over the entire density range down to half the Fermi temperature ($\theta=k_BT/E_F=0.5$) and, therefore, to compare our results to both aforementioned methods. While we find excellent agreement with CPIMC, where results are available, we observe deviations from RPIMC that are beyond the statistical errors and increase with density.