Many-body delocalization from embedded thermal inclusion

We numerically study quantum avalanches in one-dimensional disordered spin systems by attaching two XXZ spin chains. One chain has low disorder representing a rare Griffith's region, or thermal inclusion, and the second has larger disorder, i.e., disorder larger than the observed finite-size crossover. Comparing dynamics of this system to identical systems with uniformly large disorder, we find evidence for exponentially slow thermalization (in disorder) within the many-body localized regime when the rare region is present. We observe a decay of the spin imbalance in the bulk of the large disorder region that persists to long times ($\sim10^{4}$) and find a universal behavior of the spectral function.