Local Correlations in the Super Tonks-Girardeau Gas

TL;DR

This paper investigates local correlations in the super Tonks-Girardeau gas, revealing how three-body correlations behave at zero and finite temperatures, and establishing connections with relativistic field theory.

Contribution

It provides new results for local correlators in the super Tonks-Girardeau state, extending previous ground-state results to excited states and finite temperatures.

Findings

Three-body correlator matches ground-state extension results at zero temperature.

Weak temperature dependence of three-body correlator up to degeneracy temperature.

Similar three-body correlator values for super Tonks-Girardeau and repulsive Lieb-Liniger gases at high temperatures.

Abstract

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground-state of the repulsive Lieb-Liniger gas, to the super Tonks-Girardeau state. At finite temperature we obtain that the three-body correlator has a weak dependence on the temperature up to the degeneracy temperature. We also find that for temperatures larger than the degeneracy temperature the values of the three-body correlator for the super Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar even for relatively small couplings.