Algebraic construction of quantum integrable models including inhomogeneous models

TL;DR

This paper presents a unified algebraic framework for constructing a broad class of quantum integrable models, including inhomogeneous and variable mass systems, by exploiting quadratic algebra structures and quantum $R$-matrices.

Contribution

It introduces a new ancestor model based on a quadratic algebra that generates various inhomogeneous integrable models, unifying known models and creating new ones.

Findings

Constructed a new ancestor model with quadratic algebra.

Generated a wide range of integrable inhomogeneous models.

Unified classical and quantum integrable models within a single framework.

Abstract

Exploiting the quantum integrability condition we construct an ancestor model associated with a new underlying quadratic algebra. This ancestor model represents an exactly integrable quantum lattice inhomogeneous anisotropic model and at its various realizations and limits can generate a wide range of integrable models. They cover quantum lattice as well as field models associated with the quantum $R$-matrix of trigonometric type or at the undeformed $q \to 1$ limit similar models belonging to the rational class. The classical limit likewise yields the corresponding classical discrete and field models. Thus along with the generation of known integrable models in a unifying way a new class of inhomogeneous models including variable mass sine-Gordon model, inhomogeneous Toda chain, impure spin chains etc. are constructed.