Zero modes method and form factors in quantum integrable models

TL;DR

This paper introduces a method using zero modes of the monodromy matrix to derive determinant formulas for form factors in $GL(3)$-invariant quantum integrable models, simplifying their calculation.

Contribution

It establishes new relations between form factors via zero modes and shows all form factors can be derived from a single diagonal element's form factor.

Findings

Derived determinant representations for all monodromy matrix entries' form factors.

Connected form factors of different entries through zero mode relations.

Provided a unified approach to compute form factors in $GL(3)$ models.

Abstract

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. Assuming that the monodromy matrix of the model can be expanded into series with respect to the inverse spectral parameter, we define zero modes of the monodromy matrix entries as the first nontrivial coefficients of this series. Using these zero modes we establish new relations between form factors of the elements of the monodromy matrix. We prove that all of them can be obtained from the form factor of a diagonal matrix element in special limits of Bethe parameters. As a result we obtain determinant representations for form factors of all the entries of the monodromy matrix.