Resurrecting the q-deformed Haldane–Shastry model
Jules Lamers
Chalmers University
Mercredi 14/02/2018, 15:30
Salle Claude Itzykson, Bât. 774, Orme des Merisiers

\noindent ``Integrability meeting ENS/IPhT'' \\ \\ We present a new and simpler expression for the Hamiltonian of the q-deformation of the Haldane--Shastry spin chain, which was derived by D. Uglov over two decades ago in an apparently little-known preprint. While resembling the pairwise long-range form of the Haldane--Shastry model our formula accounts for the multi-spin interactions obtained by Uglov. Our expression is computationally more efficient, makes hermiticity manifest, and uncovers a relation with the Temperley--Lieb algebra. We discuss the model's properties, including its limits and q-deformed symmetries, and review the exact spectrum found by Uglov for finite spin-chain length, which parallels the isotropic case up to level splitting due to the anisotropy. We outline the proof of equality with Uglov's formulation, and comment on open puzzles and directions for the future. \\ \\ (IPhT organizers: Ivan Kostov and Didina Serban)

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