Generalized hydrodynamics of the repulsive spin-$\frac{1}{2}$ Fermi gas

TL;DR

This paper applies generalized hydrodynamics to analyze the real-time dynamics of a one-dimensional repulsive spin-1/2 Fermi gas after quantum quenches, revealing effects like spin-charge separation and polarization.

Contribution

It extends GHD to the Yang-Gaudin model, providing detailed zero- and finite-temperature analyses of non-homogeneous quenches and trap dynamics in a multi-component Fermi gas.

Findings

Characterized particle- and spin-density evolution after quenches.

Quantitative predictions for temperature, magnetic field, and chemical potential effects.

Identified signatures of spin-charge separation and polarization dynamics.

Abstract

We study non-homogeneous quantum quenches in a one-dimensional gas of repulsive spin-$1/2$ fermions, as described by the integrable Yang-Gaudin model. By means of generalized hydrodynamics (GHD), we analyze in detail the real-time evolution following a sudden change of the confining potential. We consider in particular release protocols and trap quenches, including a version of the quantum Newton's cradle. At zero temperature, we employ a simplified phase-space hydrodynamic picture to characterize the dynamics of the particle- and spin-density profiles. Away from zero temperatures, we perform a thorough numerical study of the GHD equations, and provide quantitative predictions for different values of the temperature, external magnetic field, and chemical potential. We highlight the qualitative features arising due to the multi-component nature of the elementary excitations, discussing in particular effects of spin-charge separation and dynamical polarization.