A new (in)finite dimensional algebra for quantum integrable models

TL;DR

This paper introduces a new (in)finite dimensional algebra serving as a fundamental symmetry in quantum integrable models, connecting to existing algebraic structures and offering a novel framework for analyzing both massive and conformal quantum systems.

Contribution

The paper presents a new algebraic structure that generalizes Onsager's algebra, linking it to deformed Dolan-Grady structures and providing a fresh approach to quantum integrability.

Findings

Constructed finite-dimensional representations of the algebra.

Expressed integrability quantities in terms of algebra generators.

Established relation to deformed Dolan-Grady and tridiagonal algebras.

Abstract

A new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite dimensional representations are constructed and mutually commuting quantities - which ensure the integrability of the system - are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite dimensional algebra is a ``$q-$deformed'' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models.