Unrestricted Hartree-Fock theory of Wigner crystals

TL;DR

This paper shows that unrestricted Hartree-Fock theory predicts stable Wigner crystal solutions in 2D and 3D at specific density parameters, with correlation energies significantly lower than fluid phases.

Contribution

It provides the first demonstration of stable Wigner crystal solutions within unrestricted Hartree-Fock theory for electrons in a uniform potential.

Findings

Stable Wigner crystal solutions exist for r_s ≥ 1.44 in 2D and r_s ≥ 4.5 in 3D.

Correlation energies of Wigner crystals are much smaller than those of fluid phases at the same density.

Unrestricted Hartree-Fock theory can effectively describe Wigner crystal formation.

Abstract

We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of the Wigner crystal phases are considerably smaller than those of the fluid phases at the same density.