Related papers: On a New Class of Integrable Models
Applying a unifying Lax operator approach to statistical systems a new class of integrable vertex models based on quantum algebra is proposed, which exhibits a rich variety for generic q, q roots of unity and q -> 1. Exact solutions are…
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…
We classify the completely integrable systems associated with classical root systems whose potential functions are meromorphic at an infinite point.
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…
In this letter, we continue the work we started at a previous paper and we propose new series of integrable models in quantum field theory. These models are obtained as perturbed models of the minimal conformal field theories on the…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
We introduce the notion of integrable modules over $\imath$quantum groups (a.k.a. quantum symmetric pair coideal subalgebras). After determining a presentation of such modules, we prove that each integrable module over a quantum group is…
Modular tensor categories are generalizations of the representation categories of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFTs. Although other constructions have since been found,…
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
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…
We define a "quantum spherical model", a quantum lattice model.
We collect and systematize general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems. As an example, we reconsider the case of the quantum group…
This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…
A new family of analytically solvable quantum geometric models is proposed. The structure of the energy spectra as well as the form of the corresponding eigenfunctions are presented pointing out their main specific properties.
In this paper we classify all simple weight modules for a quantum group $U_q$ at a complex root of unity $q$ when the Lie algebra is not of type $G_2$. By a weight module we mean a finitely generated $U_q$-module which has finite…
In this paper we introduce a new class of integrable 3D lattice models, possessing continuous families of commuting layer-to-layer transfer matrices. Algebraically, this commutativity is based on a very special construction of local…
We aim to explore if inside a quantum vertex algebras, we can find the right notion of a quantum conformal algebra.
This paper defines the concept of an oriented quantum algebra and develops its application to the construction of quantum link invariants. We show that all known quantum link invariants can be put into this framework.