Introduction to the Bethe Ansatz III

TL;DR

This paper uses the Bethe ansatz to analyze low-lying excitations in 1D Heisenberg antiferromagnets under magnetic fields, interpreting them as composites of different quasi-particles and predicting experimental neutron scattering spectra.

Contribution

It provides a tutorial introduction to applying the Bethe ansatz for calculating excitations and lineshapes in 1D antiferromagnetic systems, including practical problems for students.

Findings

Calculated matrix elements for low-lying excitations

Predicted neutron scattering lineshapes for quasi-1D compounds

Interpreted collective states as composites of different quasi-particles

Abstract

Having introduced the magnon in part I and the spinon in part II as the relevant quasi-particles for the interpretation of the spectrum of low-lying excitations in the one-dimensional (1D) s=1/2 Heisenberg ferromagnet and antiferromagnet, respectively, we now study the low-lying excitations of the Heisenberg antiferromagnet in a magnetic field and interpret these collective states as composites of quasi-particles from a different species. We employ the Bethe ansatz to calculate matrix elements and show how the results of such a calculation can be used to predict lineshapes for neutron scattering experiments on quasi-1D antiferromagnetic compounds. The paper is designed as a tutorial for beginning graduate students. It includes 11 problems for further study.