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arXiv:1711.03867 · SciPost Physics

Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_{n})$

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Pakuliak, E. Ragoucy, Nikita A. Slavnov

Published Jan 30, 2018• 18 citations
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Abstract

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra \uqgl{m} . We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, whose factors are characterized by two highest coefficients. We provide different recursions for these highest coefficients. In addition, we show that when the Bethe vectors are on-shell, their norm takes the form of a Gaudin determinant.

DOI
10.21468/scipostphys.4.1.006

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