Symmetry breaking in quasi-1D Coulomb systems

TL;DR

This paper proves that Coulomb systems confined to quasi-one-dimensional domains exhibit translation symmetry breaking at any temperature and finite width, extending previous results and employing a structural argument based on charge fluctuation bounds.

Contribution

It establishes symmetry breaking in quasi-1D Coulomb systems with a novel structural approach that bypasses the need for one-particle density analysis.

Findings

Symmetry breaking occurs at all temperatures and finite widths.

The method extends previous results on thin strips and Laughlin states.

Charge fluctuation bounds are key to the proof.

Abstract

Quasi one-dimensional systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g. on a cylinder of infinite length. The main result proven here is that for such particle systems with Coulomb interactions and neutralizing background, the so-called "jellium", at any temperature and at any finite-strip width there is translation symmetry breaking. This extends the previous result on Laughlin states in thin, two-dimensional strips by Jansen, Lieb and Seiler (2009). The structural argument which is used here bypasses the question of whether the translation symmetry breaking is manifest already at the level of the one particle density function. It is akin to that employed by Aizenman and Martin (1980) for a similar statement concerning symmetry breaking at all temperatures in strictly one-dimensional Coulomb systems. The extension is enabled through bounds which establish tightness of finite-volume charge fluctuations.