Thouless number and spin diffusion in quantum Heisenberg ferromagnets

TL;DR

This paper introduces a new method using the Thouless number to calculate spin diffusion coefficients in quantum Heisenberg ferromagnets, linking spin diffusion to the vanishing of the Drude peak in frequency-dependent conductance.

Contribution

It develops a novel approach based on the Thouless number to compute spin diffusion in quantum spin models, providing results across various dimensions and spins.

Findings

Spin diffusion coefficient $D_s$ is proportional to the Thouless number $g_0$.

Spin diffusion implies the vanishing of the Drude peak in $g(\, ext{omega})$.

Results obtained for $D_s$ in the infinite temperature limit for arbitrary $d$ and $S$.

Abstract

Using an analogy between the conductivity tensor of electronic systems and the spin stiffness tensor of spin systems, we introduce the concept of the Thouless number $g_0$ and the dimensionless frequency dependent conductance $g( \omega )$ for quantum spin models. It is shown that spin diffusion implies the vanishing of the Drude peak of $g ( \omega )$, and that the spin diffusion coefficient $D_s$ is proportional to $g_0$. We develop a new method based on the Thouless number to calculate $D_s$, and present results for $D_s$ in the nearest-neighbor quantum Heisenberg ferromagnet at infinite temperatures for arbitrary dimension $d$ and spin $S$.