Separation of variables in the quantum integrable models related to the Yangian Y[sl(3)]

TL;DR

This paper develops a method for separating variables in quantum integrable models associated with the Yangian Y[sl(3)], providing explicit constructions of canonical coordinates and conditions for global separation.

Contribution

It introduces a systematic approach to variable separation in Y[sl(3)] models, including explicit coordinate construction and criteria for global separation.

Findings

Constructed canonical coordinates satisfying the quantum characteristic equation

Provided conditions necessary for global separation of variables

Established a local separation framework for Y[sl(3)] models

Abstract

There being no precise definition of the quantum integrability, the separability of variables can serve as its practical substitute. For any quantum integrable model generated by the Yangian Y[sl(3)] the canonical coordinates and the conjugated operators are constructed which satisfy the ``quantum characteristic equation'' (quantum counterpart of the spectral algebraic curve for the L operator). The coordinates constructed provide a local separation of variables. The conditions are enlisted which are necessary for the global separation of variables to take place.