Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains

TL;DR

This paper studies how interactions affect localization in a disordered quantum spin chain, revealing that interactions weaken localization and lead to subdiffusive dynamics in few-particle regimes.

Contribution

It demonstrates that interactions increase localization length in disordered spin chains and identifies subdiffusive behavior in the dynamics.

Findings

Interaction increases localization length in two-particle systems.

Dynamics are subdiffusive with   t^{1/4} scaling.

Interaction effects are stronger with more particles.

Abstract

We investigate real-space localization in the few-particle regime of the XXZ spin-$1/2$ chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of non-equilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance $\sigma(t)$. For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is the stronger the more particles are taken into account in the initial condition. We further find that our non-equilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with $\sigma(t) \propto t^{1/4}$.