Reflection-Transmission Quantum Yang-Baxter Equations

TL;DR

This paper investigates the reflection-transmission quantum Yang-Baxter equations in integrable models with impurities, providing new solutions and clarifying their physical significance, thus advancing the algebraic understanding of such systems.

Contribution

It introduces three new families of solutions to the reflection-transmission quantum Yang-Baxter equations and demonstrates the universality of the reflection-transmission algebra approach.

Findings

Three general solution families are described in detail.

Explicit representatives for each solution family are provided.

The reflection-transmission algebra offers a universal framework for integrable systems with impurities.

Abstract

We explore the reflection-transmission quantum Yang-Baxter equations, arising in factorized scattering theory of integrable models with impurities. The physical origin of these equations is clarified and three general families of solutions are described in detail. Explicit representatives of each family are also displayed. These results allow to establish a direct relationship with the different previous works on the subject and make evident the advantages of the reflection-transmission algebra as an universal approach to integrable systems with impurities.