Stochastic description of the dynamics of the random-exchange Heisenberg chain

TL;DR

This paper investigates how correlated disorder affects spin-wave diffusion in a Heisenberg chain, revealing superdiffusive and ballistic behaviors that align with Hamiltonian dynamics predictions.

Contribution

It introduces a stochastic approach to describe spin-wave diffusion in disordered Heisenberg chains with power-law correlated noise, linking fluctuations to diffusion regimes.

Findings

Superdiffusive and ballistic spin-wave motions observed.

Stochastic predictions match Hamiltonian dynamics results.

Correlation in disorder influences diffusion behavior.

Abstract

We study the diffusion process in a Heisenberg chain with correlated spatial disorder, with a power spectrum in the momentum space behaving as $k^{-\beta}$, using a stochastic description. It establishes a direct connection between the fluctuation in the spin-wave density of states and the noise density of states. For continuous ranges of the exponent $\beta $, we find superdiffusive and ballistic spin-wave motions. Both diffusion exponents predicted by the stochastic procedure agree with the ones calculated using the Hamiltonian dynamics.