Andreas Klümper (U. Wuppertal) : Thermodynamics, contact and density profiles of the repulsive Gaudin-Yang model
→
Europe/Brussels
CYCL08 (MdeHemptinne)
CYCL08
MdeHemptinne
Description
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.