Finite size spectrum, magnon interactions and magnetization of S=1 Heisenberg spin chains

TL;DR

This paper combines numerical and analytical methods to analyze the finite size spectrum, magnon interactions, and magnetization properties of S=1 antiferromagnetic Heisenberg spin chains, providing insights into their critical behavior.

Contribution

It presents a detailed study of magnon interactions and finite size effects in S=1 chains, including the determination of magnon scattering length and comparison with theoretical models.

Findings

Magnon-magnon interactions significantly influence the finite size spectrum.

The magnon scattering length is quantitatively determined and compared to non-linear sigma model predictions.

Finite size effects on magnetization near the critical magnetic field are characterized.

Abstract

We report our density matrix renormalization-group and analytical work on S=1 antiferromagnetic Heisenberg spin chains. We study the finite size behavior within the framework of the non-linear sigma model. We study the effect of magnon-magnon interactions on the finite size spectrum and on the magnetization curve close to the critical magnetic field, determine the magnon scattering length and compare it to the prediction from the non-linear $\sigma$ model.