Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains

TL;DR

This paper derives transmission matrices for gl(N) and U_q(gl(N)) quantum spin chains with impurities, providing a mathematical description of particle-impurity interactions using Bethe ansatz.

Contribution

It introduces explicit transmission matrices for these models, advancing the understanding of impurity effects in integrable quantum spin chains.

Findings

Derived transmission amplitudes and matrices for models with impurities

Provided algebraic representations of particle-impurity interactions

Enhanced the mathematical framework for analyzing integrable spin chains

Abstract

The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices -representations of the underlying quadratic algebra- that physically describe the interaction between the various particle-like excitations displayed by these models and the spin impurity.