Two-Electron Correlations in the Metallic Electron Gas

TL;DR

This paper uses advanced Monte Carlo methods to analyze two-electron interactions in the electron gas, revealing a crossover in screening behavior and providing a new effective interaction model that agrees with experimental data.

Contribution

It introduces the sKO+ ansatz, a minimal correction to the charge-channel Kukkonen--Overhauser interaction, for accurate first-principles transport calculations in metals.

Findings

Identifies a density-driven crossover from underscreening to overscreening.

Provides the full two-electron scattering amplitude on the Fermi surface.

Achieves quantitative agreement with experimental thermal resistivity in simple metals.

Abstract

We present high-precision \emph{ab initio} calculations of the four-point vertex function for the three-dimensional uniform electron gas using variational diagrammatic Monte Carlo. From these results, we extract Landau parameters that reveal a density-driven crossover from underscreening to overscreening, and obtain the full two-electron scattering amplitude on the Fermi surface with controlled accuracy. A residual analysis of the scattering amplitude against the charge-channel Kukkonen--Overhauser (KO$^+$) interaction shows that only a minimal s-wave correction in the antiparallel-spin channel is needed, defining the sKO$^+$ ansatz: KO$^+$ within the local-density approximation plus this short-range correction. Using both our direct VDMC amplitudes and the sKO$^+$ ansatz, we compute the electron-electron contribution to the thermal resistivity, obtaining quantitative agreement with experiments on simple metals (Al, Na, K, Rb). sKO$^+$ thus provides a transferable effective interaction for first-principles transport calculations in metals.