Interacting finite-size magnons

TL;DR

This paper constructs and analyzes finite-volume two-magnon string solutions on R x S^2, using the O(3) sigma model and sine-Gordon theory, providing explicit energy corrections and insights into magnon interactions.

Contribution

It introduces a class of finite-volume two-magnon solutions and derives their energy corrections, connecting sigma model solutions with sine-Gordon theory.

Findings

Explicit finite-volume two-magnon solutions constructed.

Derived energy corrections for multi-magnon states.

Expressed energies in terms of action variables and scattering phases.

Abstract

We explicitly construct a large class of finite-volume two-magnon string solutions moving on R x S^2. In particular, by making use of the relationship between the O(3) sigma model and sine-Gordon theory we are able to find solutions corresponding to the periodic analogues of magnon scattering and breather-like solutions. After semi-classically quantizing these solutions we invert the implicit expressions for the excitation energies in certain limits and find the corrections for the multi-magnon states. For the breather-like solutions we express the energies directly in terms of the action variable whereas for the scattering solution we express the result as a combination of corrections to the dispersion relation and to the scattering phase.