Free from spurious solutions integral equation for three-magnon bound states in 1D XXZ ferromagnet

TL;DR

This paper introduces a new integral equation for three-magnon bound states in the 1D XXZ ferromagnet that avoids spurious solutions by using a Bloch basis decomposition, improving upon previous formulations.

Contribution

The paper presents a novel integral equation that eliminates spurious solutions in modeling three-magnon bound states in the XXZ spin chain.

Findings

The new equation successfully avoids spurious solutions.

It offers a more accurate description of three-magnon bound states.

The approach improves upon the classical equation by Majumdar.

Abstract

A new integral equation for three-magnon bound states in XXZ spin chain is suggested. Unlike the one presented by C. K. Majumdar about 40 years ago this equation does not have spurious solutions. Such an advantage is a result of decomposition of the wave function in the Bloch basis rather than in the basis of flat waves.