Analytic theory of ground-state properties of a three-dimensional electron gas at varying spin polarization

TL;DR

This paper develops an analytic approach to determine the ground-state properties of a three-dimensional electron gas with varying spin polarization, using a Schr"odinger equation and Fermi-hypernetted-chain approximation, validated against Quantum Monte Carlo data.

Contribution

It introduces a new analytic method for calculating spin-resolved pair distribution functions and ground-state energy in polarized electron gases, incorporating sum rules and the Hartree-Fock limit.

Findings

Accurate ground-state energy predictions across spin polarizations.

Good agreement with Quantum Monte Carlo data.

Validated the approach for both paramagnetic and fully spin-polarized cases.

Abstract

We present an analytic theory of the spin-resolved pair distribution functions $g_{\sigma\sigma'}(r)$ and the ground-state energy of an electron gas with an arbitrary degree of spin polarization. We first use the Hohenberg-Kohn variational principle and the von Weizs\"{a}cker-Herring ideal kinetic energy functional to derive a zero-energy scattering Schr\"{o}dinger equation for $\sqrt{g_{\sigma\sigma'}(r)}$. The solution of this equation is implemented within a Fermi-hypernetted-chain approximation which embodies the Hartree-Fock limit and is shown to satisfy an important set of sum rules. We present numerical results for the ground-state energy at selected values of the spin polarization and for $g_{\sigma\sigma'}(r)$ in both a paramagnetic and a fully spin-polarized electron gas, in comparison with the available data from Quantum Monte Carlo studies over a wide range of electron density.