Effects of Backflow Correlation in the Three-Dimensional Electron Gas: Quantum Monte Carlo Study

TL;DR

This study uses quantum Monte Carlo methods to analyze how backflow correlations influence the correlation energy in a three-dimensional electron gas, showing significant improvements in energy calculations especially at high densities.

Contribution

It demonstrates the importance of backflow correlations in accurately computing the energy of the 3D electron gas, with detailed comparisons to 2D systems and prior results.

Findings

Backflow effects dominate at high densities.

Backflow correlations improve energy estimates.

Results align with previous 2D electron gas studies.

Abstract

The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations. In the high density regime the effects of backflow dominate over those due to three-body correlations, but the relative importance of the latter increases as the density decreases. Since the backflow correlations vary the nodes of the trial function, this leads to improved energies in the fixed-node diffusion Monte Carlo calculations. The effects are comparable to those found for the two-dimensional electron gas, leading to much improved variational energies and fixed-node diffusion energies equal to the release-node energies of Ceperley and Alder within statistical and systematic errors.