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Why scalar products in the algebraic Bethe ansatz have determinant representation

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arxiv 1908.00032 v2 pith:EC3FXLQL submitted 2019-07-31 math-ph cond-mat.stat-mechhep-thmath.MP

S. Belliard , N. A. Slavnov This is my paper · ORCID
classification math-phcond-mat.stat-mechhep-thmath.MP
keywords betheansatzmodelsproductsscalarsystemalgebra1icalgebraic
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abstract

We show that the scalar products of on-shell and off-shell Bethe vectors in the algebra1ic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also apply our method to the XXX spin chain with broken $U(1)$ symmetry.

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  1. More on Slavnov Products of Spin Chains and KP Hierarchy Tau Functions

    hep-th 2025-05 reject novelty 5.0 of 10

    Slavnov products of Bethe states in rational spin chains are shown to be KP tau functions, with new Wronskian and Baker-Akhiezer formulas, but the key identification relies on an unverified assumption.

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