The Hartree-Fock ground state of the three-dimensional electron gas

TL;DR

This paper investigates the Hartree-Fock ground state of the three-dimensional electron gas, revealing a spin density wave instability at high density with a novel wave vector smaller than 2k_F, and proposes a pairing instability model.

Contribution

It provides new insights into the HF ground state of the 3D electron gas, identifying a previously uncharacterized SDW with a smaller wave vector and a pairing instability origin.

Findings

Broken spin symmetry states at high density

SDW wave vector smaller than 2k_F

Pairing instabilities at the Fermi surface

Abstract

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin density wave (SDW) instability. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the HF ground state of the 3D electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the SDW is smaller than $2 k_F$. The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.