Scaling properties of the Tan's contact: embedding pairs and correlation effect in the Tonks limit

TL;DR

This paper investigates the universal behavior of Tan's contact in a one-dimensional quantum Bose gas under strong interactions and finite temperature, revealing how pair and correlation effects are embedded in the Tonks-Girardeau limit.

Contribution

It demonstrates that the rescaled Tan's contact is a universal function of interaction strength and temperature in the strongly interacting regime.

Findings

Tan's contact rescaled by the Tonks-Girardeau limit is universal

Pair and correlation effects are embedded in the contact

Universal behavior observed at finite temperature

Abstract

We study the Tan's contact of a one dimensional quantum gas of N repulsive identical bosons confined in a harmonic trap at finite temperature. This canonical ensemble framework corresponds to the experimental conditions, the number of particles being fixed for each experimental sequence. We show that, in the strongly interacting regime, the contact rescaled by the contact at the Tonks-Girardeau limit is an universal function of two parameters, the rescaled interaction strength and temperature. This means that all pair and correlation effects in the Tan's contact are embedded in the Tan's contact in the Tonks-Girardeau limit.