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arXiv:hep-th/9609080 · Journal of Physics A Mathematical and General

On the form factors of relevant operators and their cluster property

C. Acerbi, Giuseppe Mussardo, Angelo Valleriani

Published May 7, 1997• 19 citations
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Abstract

We compute the form factors of the relevant scaling operators in a class of integrable models without internal symmetries by exploiting their cluster properties. Their identification is established by computing the corresponding anomalous dimensions by means of the Delfino - Simonetti - Cardy sum rule and further confirmed it by comparing some universal ratios of the nearby non-integrable quantum field theories with their independent numerical determination.

DOI
10.1088/0305-4470/30/9/007

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We compute the form factors of the relevant scaling operators in a class of integrable models without internal symmetries by exploiting their cluster properties. Their identification is established by computing the corresponding anomalous dimensions by means of the Delfino - Simonetti - Cardy sum rule and further confirmed it by comparing some universal ratios of the nearby non-integrable quantum field theories with their independent numerical determination.
Correlation functions of the composite field TTˉT\bar TTTˉ in the scaling Lee-Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli hep-th/0407142 [1], we show numerically that the constraints on the TTˉT\bar TTTˉ expectation values obtained by Zamolodchikov hep-th/0401146
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schrödinger model. We derive the long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle–hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on a microscopic analysis of the model, without invoking, at any stage, any correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, possibly with minor modifications, to a wide class of (not necessarily integrable) gapless one-dimensional Hamiltonians.
Correlation functions of the composite field TbarTT\\bar{T}TbarT in the scaling Lee--Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli \\cite{DN}, we show numerically that the constraints on the TbarTT\\bar{T}TbarT expectation values obtained in \\cite{AZ_VEVTT} and the additional requirement of asymptotic behavior lead to a perfect agreement with the ultraviolet asymptotic predicted by the conformal perturbation theory.
We compare two different methods of computing form factors. One is the well established procedure of solving the form factor consistency equations and the other is to represent the field content as well as the particle creation operators in terms of fermionic Fock operators. We compute the corresponding matrix elements for the complex free fermion and the Federbush model. The matrix elements only satisfy the form factor consistency equations involving anyonic factors of local commutativity when the corresponding operators are local. We carry out the ultraviolet limit, analyze the momentum space cluster properties and demonstrate how the Federbush model can be obtained from the SU(3)3-homogeneous sine-Gordon model. We propose a new class of Lagrangians which constitute a generalization of the Federbush model in a Lie algebraic fashion. For these models we evaluate the associated scattering matrices from first principles, which can alternatively also be obtained in a certain limit of the homogeneous sine-Gordon models. Based on talks presented at the conferences: “From QCD to integrable models, old results and new developments”