Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line

TL;DR

This paper develops an algebraic framework to analyze how boundary conditions in integrable quantum systems on the half line influence their symmetries, revealing instances of spontaneous symmetry breaking.

Contribution

It introduces boundary operators that encode boundary conditions and generate integrals of motion, linking boundary effects to symmetry properties in integrable systems.

Findings

Boundary operators encode boundary conditions and generate integrals of motion.

Spontaneous breakdown of some internal symmetries occurs due to boundary effects.

Framework applies to the gl(N)-NLS hierarchy on the half line.

Abstract

We describe an algebraic framework for studying the symmetry properties of integrable quantum systems on the half line. The approach is based on the introduction of boundary operators. It turns out that these operators both encode the boundary conditions and generate integrals of motion. We use this direct relationship between boundary conditions and symmetry content to establish the spontaneous breakdown of some internal symmetries, due to the boundary.