Introduction to quantum integrability
Fri, Sep. 15th 2023, 10:00-12:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
This course will give a pedagogical introduction to (quantum) integrability, a topic in mathematical physics with applications ranging from experiments in condensed-matter physics to high-energy theory. The aim is to show some highlights of the field, with a glimpse of the underlying algebraic structures, while keeping technicalities to a minimum. \\ \\ The provisional plan of the course is as follows; details can be adjusted to suit the audience. \\ Part I will cover the (standard) basics of integrability, more or less following my lecture notes arXiv:1501.06805: \\ - the Heisenberg spin chain, \\ - the six-vertex model, \\ - the exact characterisation of their spectrum by Bethe ansatz, \\ - an application to alternating-sign matrices (ASM). \\ - Part II is about the (less standard) basics of long-range integrability: \\ - the Haldane–Shastry spin chain, \\ - the quantum Calogero–Sutherland system, \\ - the exact and explicit characterisation of their spectrum.


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