Resurrecting the partially isotropic Haldane-Shastry model
Journal article, 2018

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.

Author

Jules Lamers

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Physical Review B

2469-9950 (ISSN) 2469-9969 (eISSN)

Vol. 97 21 214416

Subject Categories

Applied Mechanics

Probability Theory and Statistics

Control Engineering

DOI

10.1103/PhysRevB.97.214416

More information

Latest update

7/2/2018 2