Resurrecting the partially isotropic Haldane–Shastry model

by Jules Lamers (Chalmers University)

Tuesday 30 Jan 2018, 14:15 → 15:15 Europe/Berlin

SR3

Over two decades ago a preprint appeared in which D. Uglov obtained the partially isotropic (XXZ-like) version of the celebrated Haldane–Shastry model and found its exact spectrum. The work was never published, however, and seems to have gone largely unnoticed and been forgotten since. We present a new and simpler expression for Uglov's Hamiltonian, featuring long-range partially isotropic interactions. While resembling the pairwise form of the Haldane-Shastry model our formula accounts for the multi-spin interactions found 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 its exact spectrum for finite spin-chain length.