Bethe vectors ofGL(3)-invariant integrable models

Abstract

We study GL(3)-invariant integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian 𝒴(gl3) on the Bethe vectors are considered. These actions are relevant for the calculation of correlation functions and form factors of local operators of the underlying quantum models.

The algebraic Bethe ansatz for scalar products inSU(3)-invariant integrable models

“…However, in the case of higher rank algebras this question has not been studied yet. We will give a solution of this problem in our forthcoming publication [34].…”

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

“…However, already in the case of the gl 3 based models, we deal with three creation operators, and the form of on-shell Bethe vectors immediately becomes much more complex (see e.g. [25] and (2.14) for explicit formulas).…”

“…It is known [25][26][27]30] that a mapping φ : T (u) → T (u) is an automorphism of the RT T -algebra (2.2). Thus, the matrix T (u) satisfies the RT T -relation with the same Rmatrix (2.1).…”

Combinatorial Formulae for Nested Bethe Vectors

“…In the last expression, we develop the factor ∆ B [1] (t 1 ) · · · B [ξ 1 ] (t ξ 1 ) according to Proposition 5.3, and replace the factor ∆ ψ t 1 1 , . .…”

“…It is published with no intention to give any review of the subject or reflect the state of the art. Let us only mention a few papers making progress in particularly close problems [5,6,4,14,1,2] and those exploring recently the results of the paper [16,21,13].…”