Integrability, Non-integrability and confinement

TL;DR

This paper explores the characteristics of quantum integrable models, focusing on how integrability can be broken and the resulting confinement phenomena, using the Ising and Lieb-Liniger models as key examples.

Contribution

It compares two methods for analyzing integrability breaking, linking confinement to operator semi-locality and predicting the maximum number of bound states.

Findings

Confinement relates to the semi-locality of symmetry-breaking operators.

Bound states in broken integrability phases are limited to at most two.

The approaches provide complementary insights into non-integrable quantum models.

Abstract

We discuss the main features of quantum integrable models taking the classes of universality of the Ising model and the repulsive Lieb-Liniger model as paradigmatic examples. We address the breaking of integrability by means of two approaches, the Form Factor Perturbation Theory and semiclassical methods. Each of them has its own advantage. Using the first approach, one can relate the confinement phenomena of topological excitations to the semi-locality of the operator which breaks integrability. Using the second approach, one can control the bound states which arise in each phase of the theory and predict that their number cannot be more than two.