Universal scaling of density and momentum distributions in Lieb-Liniger gases

TL;DR

This paper investigates the universal scaling behaviors of density and momentum distributions in one-dimensional Lieb-Liniger gases, using exact numerical methods across different interaction regimes and temperatures.

Contribution

It provides a comprehensive numerical analysis of the scaling laws in trapped Lieb-Liniger gases, including the high-momentum tail behavior, bridging homogeneous and trapped cases.

Findings

Density and momentum distributions exhibit universal scaling laws.

High momentum tails follow a $k^{-4}$ decay.

Scaling behaviors are consistent across temperature regimes.

Abstract

We present an exact numerical study of the scaling of density and momentum distribution functions of harmonically trapped one-dimensional bosons with repulsive contact interactions at zero and finite temperatures. We use path integral quantum Monte Carlo with worm updates in our calculations at finite interaction strengths, and the Bose-Fermi mapping in the Tonks-Girardeau regime. We discuss the homogeneous case and, within the local density approximation, use it to motivate the scaling in the presence of a harmonic trap. For the momentum distribution function, we pay special attention to the high momentum tails and their $k^{-4}$ asymptotic behavior.