Long-time and large-distance asymptotic behavior of the current-current correlators in the non-linear Schr\"{o}dinger model

TL;DR

This paper introduces a novel method to derive the long-time and large-distance asymptotics of correlation functions in quantum integrable models, specifically applied to the non-linear Schrödinger model, revealing contributions beyond conformal field theory predictions.

Contribution

The authors develop a new approach to analyze asymptotics of correlation functions in integrable models, reducing complex calculations to simpler free fermion cases and extending understanding beyond existing conformal field theory results.

Findings

Derived asymptotic behavior of current-current correlators in the non-linear Schrödinger model.

Identified additional excitations contributing to asymptotics beyond Fermi surface predictions.

Provided explicit terms in the asymptotic expansion demonstrating the method's effectiveness.

Abstract

We present a new method allowing us to derive the long-time and large-distance asymptotic behavior of the correlations functions of quantum integrable models from their exact representations. Starting from the form factor expansion of the correlation functions in finite volume, we explain how to reduce the complexity of the computation in the so-called interacting integrable models to the one appearing in free fermion equivalent models. We apply our method to the time-dependent zero-temperature current-current correlation function in the non-linear Schr\"{o}dinger model and compute the first few terms in its asymptotic expansion. Our result goes beyond the conformal field theory based predictions: in the time-dependent case, other types of excitations than the ones on the Fermi surface contribute to the leading orders of the asymptotics.