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Resurrecting the partially isotropic Haldane-Shastry model

Journal article
Authors Jules Lamers
Published in Physical Review B
Volume 97
ISSN 2469-9950
Publication year 2018
Published at Department of Mathematical Sciences
Language en
Links https://doi.org/10.1103/PhysRevB.97...
Subject categories Probability Theory and Statistics, Control Engineering, Applied Mechanics

Abstract

© 2018 American Physical Society. We present an alternative, simpler expression for the Hamiltonian of the partially isotropic (XXZ-like) version of the Haldane-Shastry model, 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 multispin 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 model's exact 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 sln motifs.

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