Transition rates via Bethe ansatz for the spin-1/2 planar XXZ antiferromagnet

TL;DR

This paper introduces a new determinantal method to compute transition rates in the spin-1/2 XXZ antiferromagnet, providing high-precision data on dynamic spin structure factors and their singularities.

Contribution

It presents a novel determinantal representation for matrix elements of local spin operators in the XXZ model, enabling precise calculations of transition rates.

Findings

High-precision numerical data for in-plane two-spinon dynamic spin structure factor.

Identification of band edge singularities and lineshapes.

Validation of the new method against known results.

Abstract

A novel determinantal representation for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s=1/2 XXZ model is used to calculate transition rates for dynamic spin structure factors in the planar regime. In a first application, high-precision numerical data are presented for lineshapes and band edge singularities of the in-plane (xx) two-spinon dynamic spin structure factor.