Hartree-Fock Ground State Phase Diagram of Jellium

TL;DR

This paper maps the ground state phases of the three-dimensional electron gas using Hartree-Fock theory, revealing various broken symmetry states, phase transitions, and the conditions favoring different crystalline and spin configurations.

Contribution

It provides the first detailed Hartree-Fock phase diagram of 3D jellium, identifying multiple structural and spin phases across densities and their transitions.

Findings

Broken symmetry states are favored at all densities.

Incommensurate charge and spin density waves occur at high density.

Wigner crystal is favored at lower densities, with phase transitions around specific $r_s$ values.

Abstract

We calculate the ground state phase diagram of the homogeneous electron gas in three dimensions within the Hartree-Fock approximation and show that broken symmetry states are energetically favored at any density against the homogeneous Fermi gas state with isotropic Fermi surface. At high density, we find metallic spin-unpolarized solutions where electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons. For $r_s \to 0$, our solutions approach pure spin-density waves, whereas the commensurate Wigner crystal is favored at lower densities, $r_s > 3.4$. Decreasing the density, the system undergoes several structural phase transitions with different lattice symmetries. The polarization transition occurs around $r_s \approx 8.5$.