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arXiv:1210.0768 · Journal of Statistical Mechanics Theory and Experiment

Bethe vectors ofGL(3)-invariant integrable models

S. Belliard, Stanislav Zdislavovich Pakuliak, E. Ragoucy, N. A. Slavnov

Published Feb 12, 2013• 75 citations
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Abstract

We study G L (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( g l 3 ) 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.

DOI
10.1088/1742-5468/2013/02/p02020

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