Antiperiodic dynamical 6-vertex model by separation of variables II: Functional equations and form factors

TL;DR

This paper advances the analysis of the antiperiodic dynamical 6-vertex model by deriving functional equations and explicit form factors, providing a comprehensive spectral characterization and determinant formulas for local operators.

Contribution

It introduces new functional equations and reformulations for the model's spectrum, including a complete Bethe ansatz description and determinant formulas for form factors.

Findings

Complete characterization of the spectrum via discrete and functional equations

Derivation of Bethe equations for the model with an even number of sites

Determinant representations for form factors of local operators

Abstract

We pursue our study of the antiperiodic dynamical 6-vertex model using Sklyanin's separation of variables approach, allowing in the model new possible global shifts of the dynamical parameter. We show in particular that the spectrum and eigenstates of the antiperiodic transfer matrix are completely characterized by a system of discrete equations. We prove the existence of different reformulations of this characterization in terms of functional equations of Baxter's type. We notably consider the homogeneous functional $T$-$Q$ equation which is the continuous analog of the aforementioned discrete system and show, in the case of a model with an even number of sites, that the complete spectrum and eigenstates of the antiperiodic transfer matrix can equivalently be described in terms of a particular class of its $Q$-solutions, hence leading to a complete system of Bethe equations. Finally, we compute the form factors of local operators for which we obtain determinant representations in finite volume.