Introduction to Quantum Integrability

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.

56 pages, Latex. A few typos corrected

References in corpus (4)

• Integrability of quantum chains: theory and applications to the spin-1/2 $XXZ$ chain
• From affine Hecke algebras to boundary symmetries
• On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
• Contracted and expanded integrable structures

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• Introduction to classical and quantum integrability
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• Transmission amplitudes from Bethe ansatz equations
• Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Entanglement spectrum of matchgate circuits with universal and non-universal resources
• Geometric representations of braid and Yang-Baxter gates
• Comments on Slavnov products, Temperley-Lieb open spin chains, and KP tau functions
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Study of double kicked top: a classical and quantum perspective
• Selected Topics in Classical Integrability
• Freidel-Maillet type presentations of $U_q(s{l}_2)$