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arXiv · 1712.06475

A tale of two Bethe ans\"atze

Antonio Lima-Santos·Rafael I. Nepomechie·Rodrigo A. Pimenta
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Abstract

We revisit the construction of the eigenvectors of the single and double-row transfer matrices associated with the Zamolodchikov-Fateev model, within the algebraic Bethe ansatz method. The left and right eigenvectors are constructed using two different methods: the fusion technique and Tarasov's construction. A simple explicit relation between the eigenvectors from the two Bethe ans\"atze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov-Bethe vectors.

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Antonio Lima-Santos, Rafael I. Nepomechie, Rodrigo A. Pimenta. 2017-12-18. A tale of two Bethe ans\"atze. https://doi.org/10.1088/1742-5468%2Faab851

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