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

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.