Lattice Integrable Systems of Haldane-Shastry Type

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.

8 pages, NTUA 34/92

References in corpus (3)

• Exchange Operator Formalism for Integrable Systems of Particles
• On Models with Inverse-Square Exchange
• Invariants of the Haldane-Shastry $SU(N)$ Chain

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