Fig. 3.

The imbalance $\mathcal{I}$ as a function of time for different field strength and for fixed weak disorder $W=0.2$, where $L=24,\hspace{0.17em}{J}_z=J_0=1$. At $t=0$, the imbalance for each field strength starts at $\mathcal{I}\left(t=0\right)=1$. For field strengths above (and including) $F=2.0$ we cannot identify decaying behavior at these time scales. Error bars show statistical variance over 32 realizations of disorder. (Inset) The long time limit of the imbalance as a function of the field (averaged over the last 50 time steps). Below a critical value $F\lesssim F_c$ the long time limit of $\mathcal{I}$ tends to zero, while above that value the long time limit tends to a finite value that increases with the field. Notice that some of the lower $F$ curves have not yet reached their final value.