Generation of new classes of integrable quantum and statistical models

TL;DR

This paper introduces a unifying algebraic scheme to generate a broad class of integrable quantum and statistical models, including new models and solutions, by leveraging a generalized q-deformed algebra and Lax operators.

Contribution

It presents a novel algebraic framework based on q-deformation for systematically deriving both known and new integrable models and their exact solutions.

Findings

Derived new series of vertex models related to q-spin and q-boson

Unified algebraic Bethe ansatz solution for all models

Classified models based on different q values and roots of unity

Abstract

A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models and obtain new series of vertex models related to q-spin, q-boson and their hybrid combinations. Generic q, q roots of unity and q -> 1 yield different classes of integrable models. Exact solutions through algebraic Bethe ansatz is formulated for all models in a unified way.