Optimized correlations inspired by perturbation theory

TL;DR

This paper develops and tests an optimized analytical wave function method for many-electron systems, inspired by perturbation theory, achieving accurate correlation energies and structure functions especially at low densities.

Contribution

It introduces a new variant of the wave function approach that combines ladder and ring diagram summations, improving accuracy in dilute electron gases.

Findings

Accurately computes correlation energy, pair distribution, and structure functions.

Performs well in the dilute density regime.

Provides a computationally efficient approximation to fermionic many-body problems.

Abstract

We study the accuracy of analytical wave function based many-body methods derived by energy minimization of a Jastrow-Feenberg ansatz for electrons (`Fermi hypernetted chain / Euler Lagrange' approach). Approximations to avoid the complexity of the fermion problem are chosen to parallel successful boson theories and be computationally efficient. For the three-dimensional homogeneous electron gas, we calculate the correlation energy, the pair distribution function and the static structure function in comparison with simulation results. We also present a new variant of theory, which is interpreted as approximate, self-consistent sum of ladder and ring diagrams of perturbation theory. The theory performs particularly well in the highly dilute density regime.