Spin transport in the XXZ chain at finite temperature and momentum

TL;DR

This paper explores how momentum influences magnetization transport in the spin-1/2 Heisenberg chain at finite temperature, revealing a momentum-dependent diffusive regime and its dependence on temperature and anisotropy.

Contribution

It provides a combined numerical and analytical analysis of momentum-dependent diffusion in the XXZ chain at finite temperature, highlighting the conditions for diffusive behavior.

Findings

Existence of a diffusive region below a momentum cut-off

Diffusion constant scales inversely with anisotropy

Diffusion constant increases as temperature decreases

Abstract

We investigate the role of momentum for the transport of magnetization in the spin-1/2 Heisenberg chain above the isotropic point at finite temperature and momentum. Using numerical and analytical approaches, we analyze the autocorrelations of density and current and observe a finite region of the Brillouin zone with diffusive dynamics below a cut-off momentum, and a diffusion constant independent of momentum and time, which scales inversely with anisotropy. Lowering the temperature over a wide range, starting from infinity, the diffusion constant is found to increase strongly while the momentum space cut-off for diffusion decreases. Above the cut-off momentum diffusion breaks down completely.