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Lattice Integrable Systems of Haldane-Shastry Type

Alexios P. Polychronakos
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Abstract

We present a new lattice integrable system in one dimension of the Haldane-Shastry type. It consists of spins positioned at the static equilibrium positions of particles in a corresponding classical Calogero system and interacting through an exchange term with strength inversely proportional to the square of their distance. We achieve this by viewing the Haldane-Shastry system as a high-interaction limit of the Sutherland system of particles with internal degrees of freedom and identifying the same limit in a corresponding Calogero system. The commuting integrals of motion of this system are found using the exchange operator formalism.

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Alexios P. Polychronakos. 1992-10-20. Lattice Integrable Systems of Haldane-Shastry Type. https://doi.org/10.1103/physrevlett.70.2329

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