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New Family of Solvable 1D Heisenberg Models

Holger Frahm·Vladimir I. Inozemtsev
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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.

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Holger Frahm, Vladimir I. Inozemtsev. 1994-05-13. New Family of Solvable 1D Heisenberg Models. https://doi.org/10.1088/0305-4470%2F27%2F21%2F003

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