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Résumé |
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. |
