Soliton S matrices for the critical A_{N-1}^(1) chain

TL;DR

This paper computes the bulk and boundary scattering matrices for the critical A_{N-1}^(1) quantum spin chain, revealing their relation to Toda field theory and verifying boundary conditions through crossing relations.

Contribution

It provides explicit Bethe Ansatz calculations of scattering matrices and connects them to known integrable field theory results, including boundary effects.

Findings

Bulk S matrix matches soliton S matrix of A_{N-1}^(1) Toda theory

Boundary S matrix verified via generalized crossing relation

Results establish a link between spin chains and integrable field theories

Abstract

We compute by Bethe Ansatz both bulk and boundary hole scattering matrices for the critical A_{N-1}^(1) quantum spin chain. The bulk S matrix coincides with the soliton S matrix for the A_{N-1}^(1) Toda field theory with imaginary coupling. We verify our result for the boundary S matrix using a generalization of the Ghoshal-Zamolodchikov boundary crossing relation.