On the form factors of local operators in the lattice sine-Gordon model

Abstract

We develop a method for computing form factors of local operators in the framework of Sklyanin's separation of variables (SOV) approach to quantum integrable systems. For that purpose, we consider the sine-Gordon model on a finite lattice and in finite dimensional cyclic representations as our main example. We first build our two central tools for computing matrix elements of local operators, namely, a generic determinant formula for the scalar products of states in the SOV framework and the reconstruction of local fields in terms of the separate variables. The general form factors are then obtained as sums of determinants of finite dimensional matrices, their matrix elements being given as weighted sums running over the separate variables and involving the Baxter Q-operator eigenvalues.

43 pages

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• Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
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• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• SOV approach for integrable quantum models associated to general representations on spin-1/2 chains of the 8-vertex reflection algebra
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Exact finite volume expectation values of local operators in excited states
• On quantum separation of variables beyond fundamental representations
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Correlation functions by Separation of Variables: the XXX spin chain
• Aspects of the inverse problem for the Toda chain
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• On the equilibrium measure for the Lukyanov integral
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint