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

TL;DR

This paper presents a novel technique combining effective field theory and finite size scaling to precisely calculate non-universal prefactors in correlation functions of 1D quantum integrable models, with applications to three specific models.

Contribution

It introduces an exact analytic method for determining correlation function prefactors in 1D integrable models, bridging microscopic form factors with effective field theory.

Findings

Derived exact prefactors for correlation functions in Calogero-Sutherland, Lieb-Liniger, and XXZ models.

Established a unified approach combining microscopic and effective theories.

Provided explicit formulas for long-distance and dynamic response function behaviors.

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.