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.

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

“…Finally, the Bethe ansatz for Q-operators as done here is quite involved and one may suspect that there is an alternative way of doing the Bethe ansatz where the B-operators of the transfer matrix monodromy are substituted by their analogs arising from the Q-operator monodromy. In the case of higher spin transfer matrices we refer the reader to [45][46][47][48]. The action of the operator C is given through…”