Static Response of the Strongly Coupled Electron Gas from Diffusion Monte Carlo

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, rₛ≤10. In this work, we present diffusion Monte Carlo calculations of the static density response function $χ(q)$ and of $G(q)$ for 2≤ rₛ≤100, 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>kF, and extend them below kF. They also agree with diagrammatic QMC at rₛ=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.