Algebraic Bethe ansatz for $\mathfrak{o}_{2n+1}$-invariant integrable models

TL;DR

This paper develops an algebraic Bethe ansatz framework for $rak{o}_{2n+1}$-invariant integrable models, constructing Bethe vectors via Drinfeld currents and deriving their properties to facilitate scalar product analysis.

Contribution

It introduces a novel construction of Bethe vectors for $rak{o}_{2n+1}$-invariant models using Drinfeld currents and provides explicit action and recursion formulas.

Findings

Constructed Bethe vectors using Drinfeld currents.

Derived action formulas for monodromy matrix entries.

Established recursion relations for Bethe vectors.

Abstract

A class of $\mathfrak{o}_{2n+1}$-invariant quantum integrable models is investigated in the framework of algebraic Bethe ansatz method. A construction of the $\mathfrak{o}_{2n+1}$-invariant Bethe vector is proposed in terms of the Drinfeld currents for the double of Yangian $\mathcal{D}Y(\mathfrak{o}_{2n + 1})$. Action of the monodromy matrix entries onto off-shell Bethe vectors for these models is calculated. Recursion relations for these vectors were obtained. The action formulas can be used to investigate structure of the scalar products of Bethe vectors in $\mathfrak{o}_{2n+1}$-invariant models.