Scalar products of the open XYZ chain with non-diagonal boundary terms

TL;DR

This paper derives determinant formulas for scalar products and norms of Bethe states in the open XYZ chain with non-diagonal boundaries using the F-basis and Drinfeld twist, advancing the understanding of integrable quantum models.

Contribution

It provides explicit determinant representations for scalar products and norms in the open XYZ chain with non-diagonal boundary conditions, utilizing the F-basis and Drinfeld twist.

Findings

Determinant formulas for scalar products of Bethe states.

Gaudin formulas for the norms of Bethe states.

Application of the F-basis to complex boundary conditions.

Abstract

With the help of the F-basis provided by the Drinfeld twist or factorizing F-matrix of the eight-vertex solid-on-solid (SOS) model, we obtain the determinant representations of the scalar products of Bethe states for the open XYZ chain with non-diagonal boundary terms. By taking the on shell limit, we obtain the determinant representations (or Gaudin formula) of the norms of the Bethe states.