Diagrammatic Monte Carlo and GW Approximation for Jellium and Hydrogen Chain

Abstract

Within the general framework of skeleton diagrammatic expansions, the fully self-consistent GW approximation (sc-GW) is the simplest scheme based on the lowest-order diagrams. However, this established method for electronic structure calculations is rarely used in its original form when the polarization function is obtained from the product of two fully dressed single-particle Green’s functions because its most serious deficiency is known to be an incorrect prediction of the dielectric response. In this contribution, we examine the sc-GW approximation for the homogeneous electron gas and find that problems with the dielectric response are solved by enforcing the particle number conservation law in the polarization function. Our protocol for restoring physical properties of the sc-GW approximation (and more advanced schemes based on computing higher-order vertex corrections) is physically transparent and easy to implement at no additional computational cost. We further examine the accuracy of the sc-GW approximation and systematic convergence of the bold diagrammatic Monte Carlo scheme to the exact result for the single-orbital hydrogen chain system.