On Bethe vectors in mathfrak{g}{mathfrak{l}}_3 -invariant integrable models

A Liashyk,N A Slavnov

doi:10.1007/jhep06(2018)018

Abstract

We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing mathfrak{g}{mathfrak{l}}_3 -invariant R-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of these models. We prove that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters. They thus do become on-shell vectors provided the system of Bethe equations is fulfilled.

Highlights

There exist several ways to study quantum integrable models with a high rank of symmetry
We prove that the vectors constructed by this method are semi-on-shell Bethe vectors for arbitrary values of Bethe parameters
Within the framework of Quantum Inverse Scattering Method (QISM), we deal with a quantum monodromy matrix T (u), whose trace plays the role of generating functional of the integrals of motion

Summary

Introduction

There exist several ways to study quantum integrable models with a high rank of symmetry. Already in the case of the gl based models, we deal with three creation operators, and the form of on-shell Bethe vectors immediately becomes much more complex [25] and (2.14) for explicit formulas) It was observed in [1] that an operator used for constructing the SoV basis of the gl2-invariant spin chain can be used for generating the basis of the on-shell Bethe vectors. It was conjectured in [1] that a similar effect might take place in the spin chains with higher rank of symmetry. In complete analogy with the case of gl based models, on-shell Bethe vectors can be presented as a successive action of Bg(ui) onto the referent state

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Conclusion