Low-density limit of dynamical correlations in the Lieb-Liniger model

TL;DR

This paper derives explicit formulas for dynamical correlations in the Lieb-Liniger model at low particle density, valid for all space, time, and interaction strengths, providing a leading-order expansion in density.

Contribution

It introduces a new low-density expansion method for dynamical correlations in the Lieb-Liniger model, valid for all interaction strengths and space-time points.

Findings

Explicit formulas for correlations at low density

Valid for all interaction strengths $c>0$

Provides leading order in density expansion

Abstract

We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb-Liniger model, within an arbitrary eigenstate with a small particle density ${\cal D}$. They are valid for all space and time and any interaction strength $c>0$, and are the leading order of an expansion in ${\cal D}$. This expansion is obtained by writing the correlation functions as sums over form factors when formally decomposed into partial fractions.