Fig. 3.

Cross-over of the time-dependent diffusion in the noisy XXZ spin chain. Diffusion constant D(t) times Δ at infinite temperatures, obtained from MPO simulations, for the time evolution in the presence of on-site noise of strength γ at large anisotropy Δ is shown. The axes are rescaled to test the theoretical prediction in Eq. 3. For small γ and large Δ, we find good agreement; in particular, the diffusion constant saturates to a γ-independent value at long times [up to $O(\gamma /{\mathrm{\Delta }}^2)$ corrections] and is compatible with subdiffusion with $D(t)\sim t^{-1/2}$ (shown as the shaded region) for ${\gamma }^{-1}\ll t\ll {\mathrm{\Delta }}^2/\gamma$.