Exact prefactors in static and dynamic correlation functions of 1D quantum integrable models: applications to the Calogero-Sutherland, Lieb-Liniger and XXZ models

Abstract

In this article we demonstrate a recently developed technique which addresses the problem of obtaining non-universal prefactors of the correlation functions of 1D systems at zero temperature. Our approach combines the effective field theory description of generic 1D quantum liquids with the finite size scaling of form factors (matrix elements) which are obtained using microscopic techniques developed in the context of integrable models. We thus establish exact analytic forms for the prefactors of the long-distance behavior of equal time correlation functions as well as prefactors of singularities of dynamic response functions. In this article our focus is on three specific integrable models: the Calogero-Sutherland, Lieb-Liniger, and XXZ models.