Low temperature correlation functions in integrable models: Derivation of the large distance and time asymptotics from the form factor expansion

TL;DR

This paper develops a general method to derive the long-distance and long-time asymptotics of low-temperature dynamical correlation functions in integrable models with a spectral gap, classifying results based on the S matrix behavior.

Contribution

It introduces a model-independent approach analyzing singularities of operator matrix elements to determine asymptotics in integrable models with well-defined asymptotic states.

Findings

Correlation functions fall into two universality classes based on the S matrix behavior.

The approach is applicable to models with a spectral gap and well-defined asymptotic states.

Results compare and contrast with semi-classical methods by Sachdev and Young.

Abstract

We propose an approach to the problem of low but finite temperature dynamical correlation functions in integrable one-dimensional models with a spectral gap. The approach is based on the analysis of the leading singularities of the operator matrix elements and is not model specific. We discuss only models with well defined asymptotic states. For such models the long time, large distance asymptotics of the correlation functions fall into two universality classes. These classes differ primarily by whether the behavior of the two-particle S matrix at low momenta is diagonal or corresponds to pure reflection. We discuss similarities and differences between our results and results obtained by the semi-classical method suggested by Sachdev and Young, Phys. Rev. Lett. {\bf 78}, 2220 (1997).