## Introduction to the nested algebraic Bethe ansatz

N. A. Slavnov

SciPost Phys. Lect. Notes 19 (2020) · published 2 September 2020

Part of the 2018-08: Integrability in Atomic and Condensed Matter Physics Collection in the Les Houches Summer School Lecture Notes Series.

### 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.

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