The uniform quantized electron gas revisited

TL;DR

This paper revisits the correlation energy of the uniform electron gas at zero temperature using classical statistical mechanics and path integral formalism, improving upon the RPA and achieving results consistent with Monte Carlo data.

Contribution

It extends previous work by incorporating thermodynamic self-consistency into the quantized electron gas model using classical methods.

Findings

Numerical results agree well with Monte Carlo correlation energies.

Improved the RPA by focusing on thermodynamic self-consistency.

Reaffirmed the applicability of classical statistical mechanics to quantum systems.

Abstract

In this work we continue and extend our recent work on the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. As before we utilize the methods, properties, and results obtained by means of classical statistical mechanics. These were extended to quantized systems via the Feynman path integral formalism. The latter translates the quantum problem into a classical polymer problem in four dimensions. Again the well known RPA (random phase approximation) is recovered as a basic result which we then modify and improve upon. Here we will we focus upon thermodynamic self-consistency. Our numerical calculations exhibit a remarkable agreement with well known results of a standard parametrization of Monte Carlo correlation energies.