Spin diffusion of lattice fermions in one dimension

TL;DR

This paper investigates long-time spin diffusion in one-dimensional lattice fermions under harmonic trapping, revealing that spin current is driven by susceptibility effects and varies across metallic and insulating regions.

Contribution

It combines thermodynamic Bethe ansatz and local density approximation to analyze spin transport, providing new insights into the behavior of spin diffusion in trapped fermionic systems.

Findings

Spin current is driven by susceptibility effects rather than magnetization gradients.

Spin transport is absent in insulating regions and occurs only in metallic regions.

Local spin diffusion coefficient peaks at insulating regions in the weak coupling limit.

Abstract

We study long-time spin diffusion of harmonically trapped lattice fermions in one dimension. Combining thermodynamic Bethe ansatz approach and local density approximation, we calculate spin current and spin diffusion coefficient driven by the population imbalance. We find spin current is driven by susceptibility effects rather than typical diffusion where magnetization would transport from regions of high magnetization to low. As expected, spin transport is zero through insulating regions and are only present in the metallic regions. In the weak coupling limit, the local spin diffusion coefficient shows maxima at all the insulating regions. Further, we estimate damping rate of diffusion modes in the weak coupling limit within the lower metallic portion of the cloud. The predicted spin current pattern can be probed via currently available experimental techniques.