On the Problem of Spin Diffusion in 1D Antiferromagnets

TL;DR

This paper investigates spin diffusion in one-dimensional antiferromagnetic systems, revealing that pure Heisenberg chains lack diffusive excitations, but small dissipation induces diffusion, with the diffusion coefficient estimated via renormalization group methods.

Contribution

It demonstrates that spin diffusion in 1D Heisenberg chains is absent without dissipation but emerges when small dissipation is introduced, providing a method to estimate the diffusion coefficient.

Findings

Pure Heisenberg chains lack diffusive excitations.

Small dissipation induces spin diffusion.

The diffusion coefficient is estimated using renormalization group analysis.

Abstract

We study the problem of spin diffusion in magnetic systems without long-range order. We discuss the example of the 1D spin chain. For the system described by the Heisenberg Hamiltonian we show that there are no diffusive excitations. However, the addition of an arbitrarily small dissipation term, such as the spin-phonon interaction leads to diffusive excitations in the long time limit. For those excitations we estimate the spin-diffusion coefficient by means of the renormalisation group analysis.