Free Energy of the Uniform Electron Gas: Testing Analytical Models against First Principle Results

TL;DR

This paper compares various analytical models for the exchange correlation free energy of the uniform electron gas against new first-principles data, revealing significant discrepancies especially in warm dense matter conditions.

Contribution

It provides the first ab initio data for the exchange correlation free energy, enabling assessment of existing analytical models in the uniform electron gas.

Findings

Significant discrepancies found between models in warm dense matter regime.

First ab initio data for exchange correlation free energy of the uniform electron gas.

Assessment highlights the need for improved theoretical approaches.

Abstract

The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description challenging. For these reasons, over the last half century many analytical approaches have been developed the accuracy of which has remained unclear. We have recently obtained the first \textit{ab initio} data for the exchange correlation free energy of the uniform electron gas [T. Dornheim \textit{et al.}, Phys.~Rev.~Lett.~\textbf{117}, 156403 (2016)] which now provides the opportunity to assess the quality of the mentioned approaches and parametrizations. Particular emphasis is put on the warm dense matter regime, where we find significant discrepancies between the different approaches.