A tale of two Bethe ans\"atze
Mathematical Physics
2018-04-27 v2 High Energy Physics - Theory
math.MP
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.
Keywords
Cite
@article{arxiv.1712.06475,
title = {A tale of two Bethe ans\"atze},
author = {Antonio Lima-Santos and Rafael I. Nepomechie and Rodrigo A. Pimenta},
journal= {arXiv preprint arXiv:1712.06475},
year = {2018}
}
Comments
28 pages; v2: 30 pages, added proof of (4.40) and (5.39), minor changes to match the published version