Effective Static Approximation: A Fast and Reliable Tool for Warm Dense Matter Theory

TL;DR

The paper introduces an Effective Static Approximation (ESA) for the local field correction in electron gas models, enabling fast, accurate calculations of electronic properties relevant for warm dense matter and improving the interpretation of X-ray scattering experiments.

Contribution

The paper presents a novel ESA method combining neural-net representations and Monte Carlo data, enhancing the accuracy and efficiency of electronic property calculations in warm dense matter.

Findings

ESA provides more accurate inelastic scattering spectra than existing models.

Incorporation of ESA alters predictions of electronic correlations in aluminum.

ESA is suitable for integration into existing computational codes.

Abstract

We present an \emph{Effective Static Approximation} (ESA) to the local field correction (LFC) of the electron gas that enables highly accurate calculations of electronic properties like the dynamic structure factor $S(q,\omega)$, the static structure factor $S(q)$, and the interaction energy $v$. The ESA combines the recent neural-net representation [\textit{J. Chem. Phys.} \textbf{151}, 194104 (2019)] of the temperature dependent LFC in the exact static limit with a consistent large wave-number limit obtained from Quantum Monte-Carlo data of the on-top pair distribution function $g(0)$. It is suited for a straightforward integration into existing codes. We demonstrate the importance of the LFC for practical applications by re-evaluating the results of the recent {X-ray Thomson scattering experiment on aluminum} by Sperling \textit{et al.}~[\textit{Phys. Rev. Lett.} \textbf{115}, 115001 (2015)]. We find that an accurate incorporation of electronic correlations {in terms of the ESA} leads to a different prediction of the inelastic scattering spectrum than obtained from state-of-the-art models like the Mermin approach or linear-response time-dependent density functional theory. Furthermore, the ESA scheme is particularly relevant for the development of advanced exchange-correlation functionals in density functional theory.