Form factor approach to dynamical correlation functions in critical models

TL;DR

This paper introduces a form factor approach to analyze dynamical correlation functions in critical quantum integrable models, exemplified by the quantum non-linear Schrödinger model, providing first-principles results consistent with non-linear Luttinger liquid predictions.

Contribution

It develops a microscopic, first-principles method for calculating dynamical correlations in critical models, applicable beyond integrable systems.

Findings

Derived asymptotic behavior of two-point functions

Computed edge exponents and amplitudes for response functions

Confirmed non-linear Luttinger liquid predictions

Abstract

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 Schr\"odinger model. We derive 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 the microscopic analysis of the model, without invoking, at any stage, some 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, with possibly minor modifications, to a wide class of (not necessarily integrable) gapless one dimensional Hamiltonians.