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.
Highlights
The study of low-dimensional strongly correlated systems is of great importance and interest
We obtain a determinant representation of normalized scalar products of onshell and off-shell Bethe vectors in the inhomogeneous 8-vertex model
That one can take the homogeneous limit in all our formulas
Summary
The study of low-dimensional strongly correlated systems is of great importance and interest. A new method was proposed in [49], which avoids all combinatorial difficulties and allows one to reduce the calculation of scalar products of on-shell and off-shell Bethe vectors in models with the 6-vertex R-matrix to solving a system of linear equations. We obtain a system of linear equations whose solutions are the scalar products of the on-shell and off-shell Bethe vectors of the inhomogeneous 8-vertex model We find these solutions in terms of determinants (minors of the matrix of the linear system). The main content of the paper is contained, where we obtain a homogeneous system of linear equations for the scalar products of Bethe vectors, prove its solvability and solve it in terms of determinants. In appendix C we show that in the case η (the case of free fermions) even more explicit results can be obtained
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