Integrability, Duality, Monodromy, and the Structure of Bethe's Ansatz

S. Belliard, N. A. Slavnov

Abstract We consider $$ \mathfrak{g}{\mathfrak{l}}_2 $$ g l 2 -invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the actions of the twisted monodromy matrix entries on the twisted off-shell Bethe vectors.

Людвиг Дмитриевич Фаддеев

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak +4 more

We study gl(2|1) symmetric integrable models solvable by the nested algebraic Bethe ansatz.Using explicit formulas for the Bethe vectors we derive the actions of the monodromy matrix entries onto these vectors.We show that the result of these actions is a finite linear combination of Bethe vectors.The obtained formulas open a way for studying scalar products of Bethe vectors.

Tadeusz Lulek

N. A. Slavnov

Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak

We study the class of $$ \mathfrak{o} _{2n+1}$$ -invariant quantum integrable models in the framework of the algebraic Bethe ansatz and propose a construction of the $$ \mathfrak{o} _{2n+1}$$ -invariant Bethe vector in terms of the Drinfeld currents for the Yangian double $$ \mathcal{D}Y ( \mathfrak{o} _{2n+1})$$ . We calculate the action of the monodromy matrix elements on the off-shell Bethe vectors for these models and obtain recurrence relations for these vectors. The action formulas can be used to investigate scalar products of Bethe vectors in $$ \mathfrak{o} _{2n+1}$$ -invariant models.