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Scalar Products in Twisted XXX Spin Chain. Determinant Representation (1906.06897v2)
Published 17 Jun 2019 in math-ph, cond-mat.str-el, hep-th, and math.MP
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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