Resurrecting the q-deformed Haldane–Shastry model


Evan Williams
Peter Hall
Monash Road


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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 and makes hermiticity manifest. 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, which also uncovers a relation with the Temperley--Lieb algebra, and comment on open puzzles and directions for the future.


  • Dr Jules Lamers
    Dr Jules Lamers, Chalmers University of Technology