Beyond-Luttinger-liquid thermodynamics of a one-dimensional Bose gas with repulsive contact interactions

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. arXiv:1905.07391v1 [cond-mat.quant-gas]

Hole-induced anomaly in the thermodynamic behavior of a one-dimensional Bose gas

“…Equation ( 4) is an expansion for nλ 1. In the weakly-interacting regime at low temperatures T /T d √ γ 1 [33], the gas behaves as a quasicondensate and its thermodynamics can be described by the Bogoliubov (BG) theory in terms of a gas of non-interacting bosonic quasi-particles [28,34]. The specific heat per particle is [32]…”

“…[28]. The next-to-leading term in the low-p expansion of the BG spectrum, (p) ≈ v|p| 1 + p 2 /(8m 2 v 2 ) , allows to calculate the first correction beyond Luttinger Liquid [34]…”

“…For strong interactions γ 2 max π 2 , T /T d , the thermodynamics can be understood via the hard-core (HC) model [34,35]. The specific heat is then obtained from that of an ideal Fermi gas, subtracting from the system size L a "negative excluded volume" N a, where the diameter of the HC is equal to the scattering length a < 0:…”

“…The thermodynamics of a quasicondensate can be described in terms of a gas of noninteracting bosonic quasiparticles [28,34], by applying the Bogoliubov (BG) theory, whose free energy per particle is…”

“…The chemical potential, the pressure and the Tan's contact parameter have been derived in Ref. [34].…”