Broke Scale Invariance Ward Identities for the Homogeneous Electron Gas

TL;DR

This paper derives exact equations for broken scale invariance in the homogeneous electron gas, leading to a non-linear integral equation for density correlations and a hierarchy of refined equations involving plasmon correlations.

Contribution

It introduces a novel set of exact equations for broken scale invariance in the HEG, including a closed non-linear integral equation for density correlations.

Findings

Derived exact equations for broken scale invariance in HEG

Established a non-linear integral equation for density-density correlations

Developed a hierarchy of equations involving plasmon correlation functions

Abstract

We derive exact equations for a broken scale invariance of the homogeneous electron gas HEG, and show that they lead to a closed non-linear integral equation for the density- density correlation function when evaluated to leading order in the 1/N expansion. More generally, the identity leads to a sequence of more refined systems of equations, which close on a finite number of one plasmon irreducible (1PLI) correlation functions.