# Spinon decay in the spin-1/2 Heisenberg chain with weak next nearest neighbour exchange

## TL;DR

This paper investigates how weak next nearest neighbour exchange perturbations affect the stability of spinons in the spin-1/2 Heisenberg chain, finding that spinons remain well-defined despite integrability breaking.

## Contribution

It provides a leading-order calculation of spinon decay rates due to weak perturbations, revealing their robustness in a magnetic field.

## Key findings

- Spinon decay rates are small under weak perturbations.
- Spinons remain well-defined excitations despite integrability breaking.
- Dominant decay channels are identified using integrability methods.

## Abstract

Integrable models support elementary excitations with infinite lifetimes. In the spin-1/2 Heisenberg chain these are known as spinons. We consider the stability of spinons when a weak integrability breaking perturbation is added to the Heisenberg chain in a magnetic field. We focus on the case where the perturbation is a next nearest neighbour exchange interaction. We calculate the spinon decay rate in leading order in perturbation theory using methods of integrability and identify the dominant decay channels. The decay rate is found to be small, which indicates that spinons remain well-defined excitations even though integrability is broken.