Year: 2026
Type: preprint
Abstract: The local field factor $G(q)$ of the HEG describes how exchange and correlation modify the response to a static perturbation, and enters dielectric screening, effective electron--electron interactions, and the xc kernel of TDDFT. Accurate zero-temperature data for $G(q)$, however, remain limited to metallic densities, $r_s\leq10$. In this work, we present diffusion Monte Carlo calculations of the static density response function $χ(q)$ and of $G(q)$ for $2\leq r_s\leq100$, and describe and discuss the methodological steps that enabled these calculations. We show how optimization of the perturbing potential in the trial wave function has an important effect, as a poor choice can reverse the sign of the response. A closed-form expression is provided for its optimal value, together with the density dependence of the linear-response window. We further show that backflow correlations leave $χ(q)$ unchanged and that $G(q)$ depends only weakly on system size even at very low density, so that Slater--Jastrow wave functions and modest system sizes suffice. Together, these results provide a practical guide for future QMC calculations of response properties of the electron gas and real materials. Our results agree with previous DMC data at metallic densities for $q>k_F$, and extend them below $k_F$. They also agree with diagrammatic QMC at $r_s=2$. At lower densities, our results show that $G(q)$ develops a nonmonotonic structure at intermediate-$q$, where the response approaches that of the noninteracting gas. Quantitative agreement is seen with finite-temperature path integral Monte Carlo, suggesting that the previously reported finite-temperature structure is inherited from the ground state. Using a parametrization of $G(q)$ that reproduces our data throughout the liquid phase, we relate this structure to short-range order in the pair correlation function and the static structure factor.
Source: arXiv (Cornell University)
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1453181110, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, Science et Technologie à Polytechnique Paris, G2154383771, G2848635288, G3406661761, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Category I: Crossing the Divide Between Today's Practice and Tomorrow's Science, Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5212984984, G5367127336, G5464919783, G6121277264, LEAPS-MPS: Correlated Methods for Correlated Phases, G6709186444, G6754955425, G6965887028, G8174472116, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI, G8562358136, G8617358649, G8851268641
OpenAlex ID: W7224829915