Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature

TL;DR

This paper characterizes the Tan contact in a trapped Lieb-Liniger gas at finite temperature, revealing universal scaling behavior and a maximum indicating crossover to fermionization, with implications for experimental observation.

Contribution

It provides a complete characterization of the Tan contact for arbitrary interactions and temperature in a trapped Lieb-Liniger gas, combining multiple theoretical methods.

Findings

Tan contact is a universal function of two scaling parameters.

Temperature dependence of contact shows a maximum.

Maximum indicates crossover to fermionized regime.

Abstract

The universal Tan relations connect a variety of microscopic features of many-body quantum systems with two-body contact interactions to a single quantity, called the contact. The latter has become pivotal in the description of quantum gases.We provide a complete characterization of the Tan contact of the harmonically trapped Lieb-Liniger gas for arbitrary interactions and temperature.Combining thermal Bethe ansatz, local-density approximation, and exact quantum Monte Carlo calculations,we show that the contact is a universal function of only two scaling parameters, and determine the scaling function.We find that the temperature dependence of the contact, or equivalently the interaction dependence of the entropy, displays a maximum. The presence of this maximum provides an unequivocal signature of the crossover to the fermionized regime and it is accessible in current experiments.