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arXiv:1906.06897 · Symmetry Integrability and Geometry Methods and Applications

Scalar Products in Twisted XXX Spin Chain. Determinant Representation

Universit&, S. Belliard, #233, de Tours, France, Никита Андреевич Славнов

Published Sep 2, 2019• 13 citations

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.

DOI: 10.3842/sigma.2019.066

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