Scalar products of Bethe vectors in the 8-vertex model
N. Slavnov, A. Zabrodin, A. Zotov
TL;DR
This paper derives a determinant formula for scalar products of Bethe vectors in the 8-vertex model, advancing the algebraic Bethe ansatz method for integrable systems.
Contribution
It provides a new determinant representation for scalar products in the 8-vertex model using a linear equations approach.
Findings
Determinant representation of scalar products obtained
Method applicable to inhomogeneous 8-vertex model
Utilizes generalized algebraic Bethe ansatz
Abstract
We obtain a determinant representation of normalized scalar products of on-shell and off-shell Bethe vectors in the inhomogeneous 8-vertex model. We consider the case of rational anisotropy parameter and use the generalized algebraic Bethe ansatz approach. Our method is to obtain a system of linear equations for the scalar products, prove its solvability and solve it in terms of determinants of explicitly known matrices.
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