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

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.

52 pages

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Cited by in corpus (21)

• The open XXX spin chain in the SoV framework: scalar product of separate states
• On quantum separation of variables
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Separation of variables and scalar products at any rank
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• On Scalar Products in Higher Rank Quantum Separation of Variables
• On quantum separation of variables beyond fundamental representations
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• On Separation of Variables for Reflection Algebras
• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Factorization of density matrices in the critical RSOS models
• Density matrices in integrable face models
• On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Separation of variables for higher rank integrable models: review of recent progress
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint