The exact two-spinon longitudinal dynamical structure factor of the anisotropic XXZ model

TL;DR

This paper derives an exact, simple expression for the two-spinon longitudinal dynamical structure factor of the integrable XXZ model, facilitating comparison with experiments and advancing theoretical understanding.

Contribution

It provides the first explicit analytical formula for the 2-spinon longitudinal DSF of the XXZ model using quantum group methods.

Findings

Results are consistent with sum rules.

Matches isotropic and Ising limits.

Simplifies analysis of experimental data.

Abstract

Inelastic neutron scattering experiments are commonly used to unveil how excitations on Heisenberg spin models play a role in dynamical correlations functions. For a certain class of materials, like CsCoCl$_3$ or CsCoBr$_3$ salts, it turns out that their magnetic properties are fairly well approximated by quasi-one dimensional XXZ models, which enjoy the property of quantum integrability. In these instances, one can in principle use their underlying algebraic structure to describe very precisely how excitations, the so-called spinons, participate in dynamical correlations functions. Even though the available theories (either algebraic Bethe ansatz or quantum group approach) provide all the needed physical quantities such as form factors, complete set of eigenstates and spectrum, it is typically a rather daunting task, however, to obtain sufficiently simple analytical expressions for computing Dynamical Structure Factors (DSFs), valuable, e.g., for parameters estimation based on experimental data. This is particularly the case for the longitudinal DSF of the XXZ model, which has eluded a formal mathematical treatment thus far. Using the quantum group approach, we present here an exact and simple expression of the 2-spinon longitudinal DSF and show our results to be consistent with the expected sum rules and the isotropic and Ising antiferromagnet limiting cases.