Configuration Path Integral Monte Carlo Approach to the Static Density Response of the Warm Dense Electron Gas

TL;DR

This paper extends the configuration path integral Monte Carlo method to compute the static density response function of the warm dense electron gas at high to moderate densities, providing exact finite temperature results and addressing finite size errors.

Contribution

The authors develop an extension of the CPIMC formalism to inhomogeneous electron gases, enabling accurate SDRF calculations at densities beyond previous methods' reach.

Findings

First data points for SDRF at high to moderate densities using CPIMC.

Demonstration of efficient extension of CPIMC to inhomogeneous systems.

Discussion and solution for finite size errors in quantum Monte Carlo results.

Abstract

Precise knowledge of the static density response function (SDRF) of the uniform electron gas (UEG) serves as key input for numerous applications, most importantly for density functional theory beyond generalized gradient approximations. Here we extend the configuration path integral Monte Carlo (CPIMC) formalism that was previously applied to the spatially uniform electron gas to the case of an inhomogeneous electron gas by adding a spatially periodic external potential. This procedure has recently been successfully used in permutation blocking path integral Monte Carlo simulations (PB-PIMC) of the warm dense electron gas [Dornheim \textit{et al.}, Phys. Rev. E in press, arXiv:1706.00315], but this method is restricted to low and moderate densities. Implementing this procedure into CPIMC allows us to obtain exact finite temperature results for the SDRF of the electron gas at \textit{high to moderate densities} closing the gap left open by the PB-PIMC data. In this paper we demonstrate how the CPIMC formalism can be efficiently extended to the spatially inhomogeneous electron gas and present the first data points. Finally, we discuss finite size errors involved in the quantum Monte Carlo results for the SDRF in detail and present a solution how to remove them that is based on a generalization of ground state techniques.