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.
Scalar Products in Twisted XXX Spin Chain. Determinant Representation
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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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Bethe Ansatz without Nesting
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.