GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors

TL;DR

This paper derives explicit formulas for Bethe vectors in GL(3)-based quantum integrable models, demonstrating their structure as a coproduct of simpler vectors, advancing understanding of composite integrable systems.

Contribution

It provides a new explicit formula for Bethe vectors in composite models and links their structure to the coproduct property in the theory of deformed KZ equations.

Findings

Explicit Bethe vector formulas for composite models

Connection to coproduct property in deformed KZ theory

Advancement in algebraic Bethe ansatz methods

Abstract

We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable models we prove a formula for the Bethe vectors of composite model. We show that this representation is a particular case of general coproduct property of the weight functions (Bethe vectors) found in the theory of the deformed Knizhnik-Zamolodchikov equation.