Algebraic approach in unifying quantum integrable models

TL;DR

This paper introduces a new algebraic framework that unifies various quantum integrable models, including known and novel inhomogeneous and impurity models, by reducing an ancestor Lax operator.

Contribution

It presents a novel algebraic approach that unifies a broad class of quantum integrable models via reductions of an ancestor Lax operator.

Findings

Unified quantum integrable models with the same R-matrix

Derived new inhomogeneous and impurity models

Connected known models through algebraic reductions

Abstract

A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known discrete and field models a new class of inhomogeneous and impurity models are obtained.