Separation of Variables in the Classical Integrable SL(3) Magnetic Chain

TL;DR

This paper constructs a separation of variables for the classical SL(3) magnetic chain, an integrable model linked to a nonhyperelliptic algebraic curve, highlighting its role in classical and quantum integrability.

Contribution

It provides the first explicit separation of variables for the SL(3) magnetic chain, connecting classical integrability with quantum aspects.

Findings

Separation of variables is achieved for the SL(3) magnetic chain.

The model is associated with a nonhyperelliptic algebraic curve.

The work links classical separation of variables to quantum integrability.

Abstract

There are two fundamental problems studied by the theory of hamiltonian integrable systems: integration of equations of motion, and construction of action-angle variables. The third problem, however, should be added to the list: separation of variables. Though much simpler than two others, it has important relations to the quantum integrability. Separation of variables is constructed for the $SL(3)$ magnetic chain --- an example of integrable model associated to a nonhyperelliptic algebraic curve.