Principal chiral model scattering and the alternating quantum spin chain

TL;DR

This paper analyzes the scattering properties of an alternating quantum spin chain using Bethe ansatz, connecting it to principal chiral and sine-Gordon models, and providing explicit S-matrix expressions.

Contribution

It derives explicit S-matrix formulas for the critical alternating quantum spin chain and relates them to known integrable models in specific limits.

Findings

S-matrix expressions for the model obtained via Bethe ansatz

Connection to principal chiral model in the limit of large q±

Recovery of XXZ and sine-Gordon results for bound states

Abstract

We consider the critical alternating quantum spin chain with ${q_{+}\over 2}$, ${q_{-} \over2}$ spins. Using the Bethe ansatz technique we find explicit expressions for the $S$-matrix of the model. We show that in the limit that $q_{\pm} \rightarrow \infty$ our results coincide with the ones obtained for the principal chiral model level one, for the LL (RR) LR scattering. We also study the scattering of the bound states of the model and we recover the results of the XXZ (sine -Gordon) model.