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

## TL;DR

This paper thoroughly investigates the thermodynamics of a one-dimensional repulsive Bose gas beyond the Luttinger-liquid approximation, revealing non-monotonic behaviors due to non-linear dispersion and exclusion effects, with broad applicability.

## Contribution

It provides exact thermodynamic calculations using Bethe-Ansatz and interprets features through multiple analytical approaches, extending understanding beyond standard Luttinger-liquid theory.

## Key findings

- Thermodynamic quantities show non-monotonic dependence on the gas parameter.
- Non-linear dispersion and negative excluded volume effects explain opposite sign corrections.
- Predictions are applicable to various physical systems including super Tonks-Girardeau gases and quantum droplets.

## 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.