Symmetry breaking in quasi-1D Coulomb systems

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.

arXiv comment26 pages, 6 figures

References in corpus (2)

• Symmetry breaking in Laughlin's state on a cylinder
• Translation Symmetry Breaking in the One-Component Plasma on the Cylinder

Cited by in corpus (8)

• Coulomb and Riesz gases: The known and the unknown
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions
• Matrix product state representation of non-Abelian quasiholes
• Wigner crystallization in the quantum 1D jellium at all densities
• Fermionic and bosonic Laughlin state on thick cylinders
• Macroscopic and edge behavior of a planar jellium
• At the edge of a one-dimensional jellium
• Large deviations in the quantum quasi-1D jellium