Lattice Integrable Systems of Haldane-Shastry Type

TL;DR

This paper introduces a new one-dimensional lattice integrable system of the Haldane-Shastry type, derived from classical Calogero and Sutherland systems, with explicit integrals of motion.

Contribution

It presents a novel lattice integrable model of Haldane-Shastry type based on classical Calogero systems and identifies its integrals of motion using exchange operator formalism.

Findings

New lattice integrable system of Haldane-Shastry type

Explicit construction of integrals of motion

Connection between Calogero, Sutherland, and Haldane-Shastry systems

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.