Wigner crystallization in the quantum 1D jellium at all densities

TL;DR

This paper proves that in a quantum one-dimensional electron gas model, known as jellium, electrons form a Wigner crystal, breaking translational symmetry at all densities, extending previous low-density results to all densities.

Contribution

The authors demonstrate that quantum 1D jellium exhibits Wigner crystallization at all densities, generalizing prior low-density findings to a comprehensive density range.

Findings

Quantum 1D jellium breaks translational symmetry at all densities.

Wigner crystallization occurs universally in the model.

The result extends classical and low-density quantum cases.

Abstract

The jellium is a model, introduced by Wigner (1934), for a gas of electrons moving in a uniform neutralizing background of positive charge. Wigner suggested that the repulsion between electrons might lead to a broken translational symmetry. For classical one-dimensional systems this fact was proven by Kunz (1974), while in the quantum setting, Brascamp and Lieb (1975) proved translation symmetry breaking at low densities. Here, we prove translation symmetry breaking for the quantum one-dimensional jellium at all densities.