Integrability of the Inozemtsev spin chain

TL;DR

This paper proves the integrability of the Inozemtsev spin chain by constructing its conserved quantities with elliptic Dunkl operators and proposes a possible generalization.

Contribution

It demonstrates the integrability of the Inozemtsev spin chain and introduces a method to construct conserved quantities using elliptic Dunkl operators.

Findings

Inozemtsev spin chain is proven to be integrable.

Conserved quantities are explicitly constructed.

A potential generalization of the model is suggested.

Abstract

We show that the Inozemtsev spin chain is integrable. The conserved quantities (commuting Hamiltonians) are constructed using elliptic Dunkl operators. We also suggest a generalisation.