3 years ago

Resurrecting the partially isotropic Haldane-Shastry model.

Jules Lamers

Over two decades ago a preprint appeared in which D. Uglov derived the partially isotropic (XXZ-like) version of the celebrated Haldane-Shastry model and found its exact spectrum. We present a new and simpler expression for Uglov's Hamiltonian. 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 physically meaningful, makes hermiticity manifest, and is computationally more efficient. We discuss the model's properties, including its limits and (ordinary and quantum-affine) symmetries, and review the spectrum found by Uglov for finite spin-chain length, which parallels the isotropic case up to level splitting due to the anisotropy. We also extend the partially isotropic model to higher rank, with $SU(n)$ 'spins', for which the spectrum is determined by $\mathfrak{sl}_n$-motifs.

Publisher URL: http://arxiv.org/abs/1801.05728

DOI: arXiv:1801.05728v1

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