Transmission amplitudes from Bethe ansatz equations

TL;DR

This paper derives transmission amplitudes for excitations interacting with spin defects in the Heisenberg spin chain using Bethe ansatz, including breather interactions in the XXZ model, and compares results with sine-Gordon model findings.

Contribution

It provides explicit transmission amplitudes for spin chain excitations with defects, including breather interactions, using Bethe ansatz and compares with sine-Gordon results.

Findings

Transmission amplitudes for particle-defect interactions derived

Breather transmission amplitude obtained in the attractive regime

Results compared with sine-Gordon model findings

Abstract

We consider the Heisenberg spin chain in the presence of integrable spin defects. Using the Bethe ansatz methodology, we extract the associated transmission amplitudes, that describe the interaction between the particle-like excitations displayed by the models and the spin impurity. In the attractive regime of the XXZ model, we also derive the breather's transmission amplitude. We compare our findings with earlier relevant results in the context of the sine-Gordon model.