2018/01/31 by Jules Lamers · 19 citations
Chemistry · Mathematics · Physics and Astronomy · #Affine transformation #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Condensed matter physics #Geometry #Hamiltonian (control theory) #Homogeneous space #Isotropy #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Physics #Preprint #Pure mathematics #Quantum mechanics #Spin (aerodynamics) #Spins #Theoretical physics #cond-mat.str-el #hep-th #math-ph #math.MP #math.QA #nlin.SI
paper · pdf · doi:10.1103/physrevb.97.214416
published in Physical review. B./Physical review. B 97(21) (American Physical Society) · 5 pages, 1 figure, 1 table; v2: various minor changes and additions; v3: 6 pages, 1 figure, 1 table; added proof of equality of formulae, minor further changes; v4: minor changes; v5: minor change
openalex publication_date 2018/06/13 · arxiv created 2018/06/27 · arxiv updated 2018/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 \mathfraksln motifs.