Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas

Abstract

We present a thorough study of the thermodynamics of a one-dimensional repulsive Bose gas, focusing in particular on corrections beyond the Luttinger-liquid description. We compute the chemical potential, the pressure and the contact, as a function of temperature and gas parameter with exact thermal Bethe-Ansatz. In addition, we provide interpretations of the main features in the analytically tractable regimes, based on a variety of approaches (Bogoliubov, hard-core, Sommerfeld and virial). The beyond Luttinger-liquid thermodynamic effects are found to be non-monotonic as a function of gas parameter. Such behavior is explained in terms of non-linear dispersion and ``negative excluded volume'' effects, for weak and strong repulsion respectively, responsible for the opposite sign corrections in the thermal next-to-leading term of the thermodynamic quantities at low temperatures. Our predictions can be applied to other systems including super Tonks-Girardeau gases, dipolar and Rydberg atoms, helium, quantum liquid droplets in bosonic mixtures and impurities in a quantum bath.

10 pages, 3 figures

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• Exact Results for the Boundary Energy of One-Dimensional Bosons
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• Correlation properties of a one-dimensional repulsive Bose gas at finite temperature
• Scaling properties of the Tan's contact: embedding pairs and correlation effect in the Tonks limit
• Thermal fading of the $1/k^4$-tail of the momentum distribution induced by the hole anomaly
• How to measure the free energy and partition function from atom-atom correlations
• Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model
• Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model
• Particle-hole origin of thermal beating in dipole-compression modes of a 1D Bose gas