Existence of a metallic phase and upper bounds of the Hartree-Fock energy in the homogeneous electron gas

TL;DR

This paper proves that in the high-density limit, the Hartree-Fock solution for the homogeneous electron gas exhibits a metallic phase with lower energy than the Fermi gas, indicating a possible phase transition.

Contribution

It demonstrates the existence of a metallic Hartree-Fock phase in the homogeneous electron gas at large densities, supported by theoretical proof and previous simulation insights.

Findings

Hartree-Fock solution has lower energy than Fermi gas at large densities

The metallic phase involves a partially occupied crystal structure

Supports the existence of a phase transition in the electron gas

Abstract

We consider the ground state of the homogeneous electron gas and we prove that a Hartree-Fock solution, motivated by previous simulations, has lower energy than the Fermi gas in the large density limit. This solution is a metallic phase : the density modulation corresponds to a partially occupied crystal (the number of sites is larger than the number of electrons).