Nonuniversal prefactors in correlation functions of 1D quantum liquids

TL;DR

This paper introduces a new method to compute nonuniversal prefactors in correlation functions of 1D quantum liquids by linking them to finite size scaling of form factors, applicable to both perturbative and exactly solvable models.

Contribution

It presents a general approach to determine nonuniversal prefactors in 1D quantum liquids, connecting finite size effects to correlation function amplitudes, including perturbative and non-perturbative cases.

Findings

Derived a relation between prefactors and finite size scaling of form factors.

Perturbatively calculated prefactors for weakly interacting spinless fermions.

Non-perturbative evaluation of prefactors in the Lieb-Liniger model.

Abstract

We develop a general approach to calculating "nonuniversal" prefactors in static and dynamic correlation functions of 1D quantum liquids at zero temperature, by relating them to the finite size scaling of certain matrix elements (form factors). This represents a new, powerful tool for extracting data valid in the thermodynamic limit from finite-size effects. As the main application, we consider weakly interacting spinless fermions with an arbitrary pair interaction potential, for which we perturbatively calculate certain prefactors in static and dynamic correlation functions. We also non-perturbatively evaluate prefactors of the long-distance behavior of correlation functions for the exactly solvable Lieb-Liniger model of 1D bosons.