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

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 [S. Sachdev, A.P. Young, Phys. Rev. Lett. 78 (1997) 2220].