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arXiv:1008.3810 · Journal of Statistical Mechanics Theory and Experiment

Form factor expansion for thermal correlators

Balázs Pozsgay, G. Takács

Published Nov 9, 2010• 97 citations
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Abstract

We consider finite temperature correlation functions in massive integrable quantum field theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair–Mussardo proposal.

DOI
10.1088/1742-5468/2010/11/p11012

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We consider finite temperature correlation functions in massive integrable quantum field theory. Using a regularization by putting the system in finite volume, we develop a novel approach (based on multi-dimensional residues) to the form factor expansion for thermal correlators. The first few terms are obtained explicitly in theories with diagonal scattering. We also discuss the validity of the LeClair–Mussardo proposal.
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Abstract We study the form factors of local operators of integrable QFT’s between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov’s form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.
We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.
We review the concept of finite-temperature form factor that was introduced recently by the author in the context of the Majorana theory.Finite-temperature form factors can be used to obtain spectral decompositions of finite-temperature correlation functions in a way that mimics the form-factor expansion of the zero temperature case.We develop the concept in the general factorised scattering set-up of integrable quantum field theory, list certain expected properties and present the full construction in the case of the massive Majorana theory, including how it can be applied to the calculation of correlation functions in the quantum Ising model.In particular, we include the "twisted construction", which was not developed before and which is essential for the application to the quantum Ising model.