Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas

TL;DR

This paper analytically investigates the momentum distribution and high-order correlation functions of the 1D strongly interacting Bose gas using the Lieb-Liniger model, revealing universal relations and the impact of interaction strength.

Contribution

It introduces analytical methods to compute local and nonlocal correlation functions and momentum distribution in the Lieb-Liniger model, emphasizing the fractional statistical parameter's role.

Findings

Analytical expressions for two-point correlation functions.

Large momentum tail characterized by fractional statistical parameter.

Universal relations such as Tan's adiabatic relation derived for the model.

Abstract

The Lieb-Liniger model is a prototypical integrable model and has been turned into the benchmark physics in theoretical and numerical investigations of low dimensional quantum systems. In this note, we present various methods for calculating local and nonlocal $M$-particle correlation functions, momentum distribution and static structure factor. In particular, using the Bethe ansatz wave function of the strong coupling Lieb-Liniger model, we analytically calculate two-point correlation function, the large moment tail of momentum distribution and static structure factor of the model in terms of the fractional statistical parameter $\alpha =1-2/\gamma$, where $\gamma$ is the dimensionless interaction strength. We also discuss the Tan's adiabatic relation and other universal relations for the strongly repulsive Lieb-Liniger model in term of the fractional statistical parameter.