Quantum integrability and quantum groups

Abstract

Abstract This report presents a brief summary of the theory of quantum integrable systems. First, the quantum inverse scattering method is used to give an algebraic formulation of the Bethe ansatz method. Second, the Yang-Baxter relation, a sufficient condition for integrability, is introduced and its relation to quantum groups is discussed. Third, some recent results on quantum integrable systems with long-range interactions are explained. To present the basic ideas and concepts in an introductory way, specific models are chosen. The results, however, apply to a wider class of quantum integrable models.