New Family of Solvable 1D Heisenberg Models

Abstract

Starting from a Calogero--Sutherland model with hyperbolic interaction confined by an external field with Morse potential we construct a Heisenberg spin chain with exchange interaction $\propto 1/{\sinh }^{2}x$ on a lattice given in terms of the zeroes of Laguerre polynomials. Varying the strength of the Morse potential the Haldane--Shastry and harmonic spin chains are reproduced. The spectrum of the models in this class is found to be that of a classical one-dimensional Ising chain with nonuniform nearest neighbour coupling in a nonuniform magnetic field which allows to study the thermodynamics in the limit of infinite chains.

8 pp, LaTeX, ITP-UH-07/94

References in corpus (6)

• Exchange Operator Formalism for Integrable Systems of Particles
• Lattice Integrable Systems of Haldane-Shastry Type
• Solution of Some Integrable One-Dimensional Quantum Systems
• Exact Spectrum of SU(n) Spin Chain with Inverse-Square Exchange
• Spectrum of a spin chain with inverse square exchange
• Invariants of the Haldane-Shastry $SU(N)$ Chain

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