Introduction to the nested algebraic Bethe ansatz

TL;DR

This paper provides a comprehensive overview of the nested algebraic Bethe ansatz, focusing on models with a gl_3-invariant R-matrix, including explicit formulas, recursions, and trace representations for Bethe vectors.

Contribution

It offers detailed formulas, recursions, and trace representations for Bethe vectors in nested algebraic Bethe ansatz, expanding understanding of gl_3-invariant models.

Findings

Explicit formulas for Bethe vectors

Recursion relations for Bethe vectors

Trace formula representation of Bethe vectors

Abstract

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions and explicit formulas for the Bethe vectors. We also give a representation for the Bethe vectors in the form of a trace formula.