Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation

TL;DR

This paper derives a determinant formula for scalar products of Bethe vectors in models with rak{gl}(2|1) symmetry, enabling calculation of norms and form factors even when Bethe parameters do not satisfy the Bethe equations.

Contribution

It provides a new determinant representation for scalar products of Bethe vectors under weaker conditions than the Bethe equations in rak{gl}(2|1) models.

Findings

Determinant formulas for scalar products and norms of Bethe vectors.

Explicit expressions for form factors of monodromy matrix entries.

Applicable to models with rak{gl}(2|1) symmetry, broadening computational tools.

Abstract

We study integrable models with $\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the Bethe parameters obey some relations weaker than the Bethe equations. This representation allows us to find the norms of on-shell Bethe vectors and obtain determinant formulas for form factors of the diagonal entries of the monodromy matrix.