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

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arxiv 1803.07628 v1 pith:XRDDISAO submitted 2018-03-20 math-ph cond-mat.stat-mechhep-thmath.MP

A. Liashyk , N. A. Slavnov This is my paper · ORCID
classification math-phcond-mat.stat-mechhep-thmath.MP
keywords bethevectorsmodelsintegrableinvariantmathfrakon-shellalgebraic
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abstract

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

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  1. Bethe Ansatz without Nesting

    hep-th 2026-07 accept novelty 7.0 of 10

    Non-nested Bethe equations for gl_ℓ vector spin chains encode the full spectrum in the roots of Q1(u) alone via a hierarchy of transfer-matrix regularity conditions closing at R_ℓ=0.

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