Introduction to Quantum Integrability

TL;DR

This paper reviews fundamental concepts of quantum integrability, focusing on algebraic structures like the Yang-Baxter equations, quantum groups, and the algebraic Bethe ansatz, highlighting their interrelations and significance.

Contribution

It provides a comprehensive overview of the algebraic framework of quantum integrable models, emphasizing the role of Yang-Baxter equations and quantum groups.

Findings

Clarifies the algebraic structure of integrable models

Explains the connection between Yang-Baxter equations and braid groups

Summarizes the quantum inverse scattering method

Abstract

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 Yang-Baxter equations depending on the choice of boundary conditions. The relation between the aforementioned equations and the braid group is briefly discussed. A short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.