GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators

TL;DR

This paper develops a method to compute form factors of local operators in GL(3)-based quantum integrable models using a composite approach and determinant representations, advancing the inverse scattering problem solution.

Contribution

It introduces a novel approach to calculate matrix elements of local operators in nested algebraic Bethe ansatz models with GL(3) symmetry, providing determinant formulas.

Findings

Derived determinant representations for form factors.

Solved the inverse scattering problem in a weak sense.

Extended the understanding of local operator matrix elements in GL(3) models.

Abstract

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial monodromy matrices. Assuming that the last ones can be expanded into series with respect to the inverse spectral parameter we calculate matrix elements of the local operators in the basis of the transfer matrix eigenstates. We obtain determinant representations for these matrix elements. Thus, we solve the inverse scattering problem in a weak sense.