Real-time spin-charge separation in one-dimensional Fermi gases from generalized hydrodynamics

TL;DR

This paper demonstrates how generalized hydrodynamics can be used to observe and analyze spin-charge separation in one-dimensional Fermi gases, revealing the dynamics at various temperatures and interaction strengths.

Contribution

It provides an exact hydrodynamic analysis of spin-charge separation in 1D Fermi gases, including finite temperature effects and the conditions under which SCS persists or melts.

Findings

Spin and charge decouple dynamically after a transient regime at zero temperature.

Finite temperature effects can be quantitatively characterized, showing the persistence or melting of SCS.

The results are understood through a phase-space hydrodynamic picture.

Abstract

We revisit early suggestions to observe spin-charge separation (SCS) in cold-atom settings {in the time domain} by studying one-dimensional repulsive Fermi gases in a harmonic potential, where pulse perturbations are initially created at the center of the trap. We analyze the subsequent evolution using generalized hydrodynamics (GHD), which provides an exact description, at large space-time scales, for arbitrary temperature $T$, particle density, and interactions. At $T=0$ and vanishing magnetic field, we find that, after a nontrivial transient regime, spin and charge dynamically decouple up to perturbatively small corrections which we quantify. In this limit, our results can be understood based on a simple phase-space hydrodynamic picture. At finite temperature, we solve numerically the GHD equations, showing that for low $T>0$ effects of SCS survive and {characterize} explicitly the value of $T$ for which the two distinguishable excitations melt.