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.
Highlights
Gapless systems in one spatial dimension often feature a linear phononic spectrum at low momenta and this strongly constrains the low-temperature thermodynamics
The same trend is visible in the first correction to the leading classical gas contribution at high T
We provided a complete study of the chemical potential, pressure, and contact as a function of temperature and interaction strength for a 1D Bose gas with repulsive contact interactions
Summary
Gapless systems in one spatial dimension often feature a linear phononic spectrum at low momenta and this strongly constrains the low-temperature thermodynamics. In the opposite TG regime, the upper and the lower branches coincide with the particle and hole excitations of the ideal Fermi gas, respectively [5] Such complex structure has not permitted, so far, an easy physical interpretation of its effects on the corresponding thermodynamic behavior. The results are reported as ratios of the observables to their values given by the LL theory With this choice, at low T , they all converge to unity for any value of the interaction strength γ , while, at higher T , any deviation from Luttinger-liquid line quantifies beyond-LL behavior which, instead, is strongly affected by γ. In the rest of the paper, we provide the understanding of dominant effects in the regimes which may be treated analytically
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