A tale of two Bethe ansätze. (26th April 2018)

• Record Type: Journal Article
• Authors: Lima-Santos, Antonio; Nepomechie, Rafael I; Pimenta, Rodrigo A
• Is Part Of: Journal of statistical mechanics. (2018:Apr.)
• Publication Date: 2018-04-26
• Subjects: 1; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/aab851
• Languages: English
• ISSNs: 1742-5468

Abstract

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 ansätze is obtained. As a consequence, we obtain the Slavnov formula for the scalar product between on-shell and off-shell Tarasov–Bethe vectors.