Diagonal solutions to reflection equations in higher spin XXZ model

TL;DR

This paper introduces a fusion method for deriving diagonal solutions to reflection equations in higher spin XXZ models, demonstrated on spin chains and extended to higher rank algebras like su(3).

Contribution

The paper presents a new fusion approach to find reflection equation solutions in higher spin and higher rank algebra models, expanding the toolkit for integrable systems.

Findings

Derived diagonal K-matrices for alternating spin chains.

Applied the method to higher rank algebra representations.

Provided explicit Hamiltonians for the models.

Abstract

A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the $K$ diagonal boundary matrices in an alternating spin $1/2$ and spin $1$ chain. The hamiltonian is also given. The applicability of the method to higher rank algebras is shown by obtaining the $K$ diagonal matrices for a spin chain in the $\left\{ 3^* \right\}$ representation of $su(3)$ from the $\left\{ 3\right\}$ representation.