The Hartree-Fock phase diagram of the two-dimensional electron gas

TL;DR

This paper maps the phase diagram of a 2D electron gas using Hartree-Fock theory, revealing incommensurate crystal phases at high density and Wigner crystal at low density, showing the homogeneous Fermi liquid is never the ground state.

Contribution

It provides the first detailed Hartree-Fock phase diagram for the 2D electron gas, identifying stable phases across densities and clarifying the ground state nature.

Findings

Incommensurate crystal phases exist at high densities.

Wigner crystal is favored at densities rs > 1.22.

Homogeneous Fermi liquid is not the Hartree-Fock ground state.

Abstract

We calculate the ground state phase diagram of the homogeneous electron gas in two dimensions within the Hartree-Fock approximation. At high density, we find stable solutions, where the electronic charge and spin density form an incommensurate crystal having more crystal sites than electrons, whereas the commensurate Wigner crystal is favored at lower densities, rs> 1.22. Our explicit calculations demonstrate that the homogeneous Fermi liquid state -- though being an exact stationary solution of the Hartree-Fock equations -- is never the Hartree-Fock ground state of the electron gas.