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Scalar Products in Twisted XXX Spin Chain. Determinant Representation

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arxiv 1906.06897 v2 pith:HZ6JJWFS submitted 2019-06-17 math-ph cond-mat.str-elhep-thmath.MP

Samuel Belliard , Nikita A. Slavnov This is my paper · ORCID
classification math-phcond-mat.str-elhep-thmath.MP
keywords bethedeterminanton-shellrepresentationvectorschainobtainscalar
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abstract

We consider XXX spin-$1/2$ Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors are on shell, we obtain a determinant representation for the norm of on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. OpenAlex reports about 13 citations worldwide. Full citation record

  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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