Aspects of Confinement in Low Dimensions

TL;DR

This paper reviews confinement phenomena in low-dimensional condensed matter systems, focusing on the off-critical Ising model and coupled Hubbard chains, highlighting how elementary excitations form mesons and how quantum techniques provide insights.

Contribution

It provides a comparative analysis of confinement in different low-dimensional models using quantum mechanics and form factor methods, emphasizing their non-integrable nature.

Findings

Elementary excitations are confined into mesons in the studied models.

Quantum mechanics and form factor techniques yield valuable insights despite non-integrability.

Confinement phenomena are exemplified in both 1+1 and quasi-one-dimensional systems.

Abstract

We briefly review some examples of confinement which arise in condensed matter physics. We focus on two instructive cases: the off-critical Ising model in a magnetic field, and an array of weakly coupled (extended) Hubbard chains in the Wigner crystal phase. In the appropriate regime, the elementary excitations in these 1+1 and quasi-one-dimensional systems are confined into `mesons'. Although the models are generically non-integrable, quantum mechanics and form factor techniques yield valuable information.