A tale of two Bethe ansätze

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.

arXiv comment28 pages; v2: 30 pages, added proof of (4.40) and (5.39), minor changes to match the published version

References in corpus (11)

• Form factors of the XXZ Heisenberg spin-1/2 finite chain
• Correlation functions of the higher spin XXX chains
• Bethe Ansatze for 19-vertex Models
• Scale invariant transfer matrices and Hamiltionians
• Algebraic Bethe Ansatz for the Zamolodchikov-Fateev and Izergin-Korepin models with open boundary conditions
• Form factors of integrable higher-spin XXZ chains and the affine quantum-group symmetry
• Correlation functions of the integrable isotropic spin-1 chain at finite temperature
• Nonstandard coproducts and the Izergin-Korepin open spin chain
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• Fusion for the one-dimensional Hubbard model
• Fusion for AdS/CFT boundary S-matrices

Cited by in corpus (1)

• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin