Variational perturbation approach to the Coulomb electron gas

TL;DR

This paper evaluates a variational perturbation method for the 3D Coulomb electron gas, showing it yields more accurate correlation energies than traditional approaches by summing variational ring diagrams.

Contribution

It introduces a systematic way to perform perturbations beyond variational results using a modified Wick's theorem, improving correlation energy calculations.

Findings

Correlation energy closely matches Monte Carlo results.

Variational ring diagrams improve accuracy over conventional methods.

Method enhances systematic perturbation calculations for many-particle systems.

Abstract

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.