Regensburg 2016 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 53: Low-Dimensional Systems: 1D - Theory
TT 53.9: Vortrag
Mittwoch, 9. März 2016, 17:15–17:30, H23
Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model — •Andreas Klümper1 and Ovidiu Patu2 — 1Universität Wuppertal, Gauss-Strasse 20, 42119 Wuppertal — 2Institute for Space Sciences, Bucharest-Magurele, R 077125
We address the problem of computing the thermodynamic properties of the repulsive one-dimensional two-component Fermi gas with contact interaction (Gaudin-Yang model). We derive an exact system of only two non-linear integral equations for the thermodynamics of the homogeneous model. This system allows for an easy and extremely accurate calculation of thermodynamic properties circumventing the difficulties associated with the truncation of the thermodynamic Bethe ansatz system of equations. We present extensive results for the densities, polarization, magnetic susceptibility, specific heat, interaction energy, Tan contact and local correlation function of opposite spins. Our results show that at low and intermediate temperatures the experimentally accessible contact is a non-monotonic function of the coupling strength. As a function of the temperature the contact presents a pronounced local minimum in the Tonks-Girardeau regime which signals an abrupt change of the momentum distribution in a small interval of temperature. The density profiles of the system in the presence of a harmonic trapping potential are computed using the exact solution of the homogeneous model coupled with the local density approximation. At finite temperature the density profile presents a double shell structure (partially polarized centre and fully polarized wings) only when the polarization in the center of the trap is above a critical value.