On Bethe vectors in gl3 $$ \mathfrak{g}{\mathfrak{l}}_3 $$-invariant integrable models

Abstract

Abstract We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl3 $$ \mathfrak{g}{\mathfrak{l}}_3 $$-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.

Keywords

• Integrable Field Theories
• Lattice Integrable Models