Spin-charge separation effects in the low-temperature transport of one-dimensional Fermi gases

We study the transport properties of a one-dimensional spinful Fermi gas, after a junction of two semi-infinite subsystems held at different temperatures. The ensuing dynamics is studied by analyzing the space-time profiles of local observables emerging at large distances x and times t, as a function of ζ=x/t. At equilibrium, the system displays two distinct species of quasiparticles, naturally associated with different physical degrees of freedom. By employing the generalized hydrodynamic approach, we show that when the temperatures are finite no notion of separation can be attributed to the quasiparticles. In this case, the profiles can not be qualitatively distinguished by those associated to quasiparticles of a single species that can form bound states. On the contrary, signatures of separation emerge in the low-temperature regime, where two distinct characteristic velocities appear. In this regime, we analytically show that the profiles display a piecewise constant form and can be understood in terms of two decoupled Luttinger liquids.