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arXiv:1907.11875

New approach to scalar products of Bethe vectors

Andrii Nikolaevich Liashyk

Published Jul 27, 2019• 0 citations
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Abstract

We consider quantum integrable models solvable by the algebraic Bethe ansatz and possessing $\mathfrak{gl}(2)$-invariant $R$-matrix. We study the models of both periodic boundary conditions and boundary conditions based on reflection algebra. We present a new method to calculate the scalar products based on formula of an action of transfer matrix of a model onto Bethe vector. Using this method we identify some coefficient in the multiple action of the transfer matrix with the scalar product between on-shell and off-shell Bethe vectors. This allows us to find determinant representation of the scalar products in both types of boundary conditions.

DOI
10.48550/arxiv.1907.11875

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