Three magnons in an isotropic $S=1$ ferromagnetic chain as an exactly solvable non-integrable system

TL;DR

This paper introduces an exact solution method for the three-magnon problem in an isotropic S=1 ferromagnetic chain using a generalized Bethe Ansatz, highlighting a novel approach to non-integrable systems.

Contribution

It presents a generalized Bethe Ansatz based on degenerative discrete-diffractive wave functions to solve the three-magnon problem in a non-integrable S=1 ferromagnetic chain.

Findings

Successfully solves the three-magnon problem using the new Ansatz.

Discusses potential extension to four-magnon problem.

Provides insights into non-integrable quantum spin systems.

Abstract

It is shown that a generalization of Bethe Ansatz based on an utilization of {\it degenerative discrete-diffractive} wave functions solves the three-magnon problem for the $S=1$ isotropic ferromagnetic infinite chain. The four-magnon problem is briefly discussed.