Effective electronic forces and potentials from ab initio path integral Monte Carlo simulations

TL;DR

This paper provides highly accurate ab initio path integral Monte Carlo results for effective electron-electron interactions in the uniform electron gas, revealing finite-size effects and an effective attraction without ionic mediation, useful for benchmarking and methodological advances.

Contribution

The work offers the first comprehensive ab initio PIMC data for effective electron interactions in the UEG, including direct evidence of attraction and comparison with linear-response theory.

Findings

Confirmed effective attraction between electrons under moderate coupling.

Provided benchmark data for effective potentials in the uniform electron gas.

Analyzed finite-size effects and their implications for many-body simulations.

Abstract

The rigorous description of correlated quantum many-body systems constitutes one of the most challenging tasks in contemporary physics and related disciplines. In this context, a particularly useful tool is the concept of effective pair potentials that take into account the effects of the complex many-body medium consistently. In this work, we present extensive, highly accurate \emph{ab initio} path integral Monte Carlo (PIMC) results for the effective interaction and the effective force between two electrons in the presence of the uniform electron gas (UEG). This gives us a direct insight into finite-size effects, thereby opening up the possibility for novel domain decompositions and methodological advances. In addition, we present unassailable numerical proof for an effective attraction between two electrons under moderate coupling conditions, without the mediation of an underlying ionic structure. Finally, we compare our exact PIMC results to effective potentials from linear-response theory, and we demonstrate their usefulness for the description of the dynamic structure factor. All PIMC results are made freely available online and can be used as a thorough benchmark for new developments and approximations.