Form factor approach to the asymptotic behavior of correlation functions in critical models

TL;DR

This paper introduces a form factor method to accurately compute the asymptotic behavior of correlation functions in quantum critical models, aligning with predictions from conformal field theory and Luttinger liquids.

Contribution

It develops a novel approach that reduces complex sums over excited states to critical form factors, enabling precise asymptotic analysis in integrable and potentially non-integrable models.

Findings

Exact computation of large-distance asymptotics for correlation functions.

Validation of results against conformal field theory and Luttinger liquid predictions.

Applicability to a broad class of quantum critical models.

Abstract

We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Luttinger liquid approach, the conformal field theory predictions and our previous analysis of the correlation functions from their multiple integral representations. We argue that our scheme applies to a general class of non-integrable quantum critical models as well.