Correlation energy of an electron gas: a functional approach

TL;DR

This paper introduces a functional approach using Effective Action to analyze correlation energies in an electron gas, incorporating corrections beyond RPA and aligning well with numerical results.

Contribution

It develops a novel functional method based on Effective Action that explicitly depends on two-point correlation functions, extending beyond traditional RPA approximations.

Findings

Agreement with known numerical calculations

Inclusion of exchange effects on ring diagrams

Potential application to non-homogeneous electron systems

Abstract

Correlation effects of an electron gas in an external potential are derived using an Effective Action functional method. Corrections beyond the random phase approximation (RPA) are naturally incorporated by this method. The Effective Action functional is made to depend explicitly on two-point correlation functions. The calculation is carried out at imaginary time. For a homogeneous electron gas, we calculate the effect of exchange on the ring diagrams at zero temperature and show how to include some of the ladder diagrams. Our results agree well with known numerical calculations. We conclude by showing that this method is in fact a variant of the time dependent density functional method and suggest that it is suitable to be applied to the study of correlation effects in the non-homogeneous case.