Integrable $1/r^2$ Spin Chain with Reflecting End

Abstract

A new integrable spin chain of the Haldane-Shastry type is introduced. It is interpreted as the inverse-square interacting spin chain with a {\it reflecting end}. The lattice points of this model consist of the square roots of the zeros of the Laguerre polynomial. Using the ``exchange operator formalism'', the integrals of motion for the model are explicitly constructed.

13 pages, REVTeX3, with minor corrections

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Cited by in corpus (30)

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• The Berry-Tabor conjecture for spin chains of Haldane-Shastry type
• Exactly solvable D_N-type quantum spin models with long-range interaction
• An exactly solvable supersymmetric spin chain of BC_N type
• On the level density of spin chains of Haldane--Shastry type
• Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime
• Inozemtsev's hyperbolic spin model and its related spin chain
• On the Sutherland Spin Model of B_N Type and its Associated Spin Chain
• Thermodynamics of spin chains of Haldane-Shastry type and one-dimensional vertex models
• Two limiting regimes of interacting Bessel processes
• Symmetric Functions and B_N-invariant Spherical Harmonics
• Spectral properties of supersymmetric Polychronakos spin chain associated with A_{N-1} root system
• The spin Sutherland model of D_N type and its associated spin chain
• Solvable scalar and spin models with near-neighbors interactions
• Universal Lax pairs for Spin Calogero-Moser Models and Spin Exchange Models
• The exactly solvable spin Sutherland model of B_N type and its related spin chain
• Spin chains of Haldane-Shastry type and a generalized central limit theorem
• $1/f^{\alpha }$ noise and integrable systems
• Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators
• Planar Harmonic Polynomials of Type B
• Hierarchies of Spin Models related to Calogero-Moser Models
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Supersymmetric analogue of BC_N type rational integrable models with polarized spin reversal operators
• Rational quantum integrable systems of D_N type with polarized spin reversal operators
• The open Haldane-Shastry chain: thermodynamics and criticality
• Super Rogers-Szegö polynomials associated with $B{C}_N$ type of Polychronakos spin chains
• A Haldane-Shastry spin chain of BC_N type in a constant magnetic field