Propagation of avalanches in the disordered Heisenberg model: a computational study

The transition from ergodic to many-body localized phases is believed to be driven by an avalanche mechanism. In this process, thermalized regions form due to disorder fluctuations, promoting thermalization of their vicinity and consequent system delocalization, unless the disorder strength is sufficient to inhibit this process. We consider the XXZ model with uniform disorder in contact with a weakly disordered spin chain, comprising a finite thermal bath. By inspecting the time evolution of the two-body spin correlation functions with the bath, we are able to capture thermal avalanches spreading through the system, or a lack thereof, depending on the disorder strengths and system sizes. We also confirm that a weakly disordered bath Hamiltonian can be well approximated by a Gaussian Orthogonal Ensemble random matrix upon a proper energy rescaling. Finally, we comment on the recent result of Peacock and Sels (PRB 108, L020201 (2023)), noticing that a universal thermalizing behavior caused by a thermal inclusion may be an effect of the lack of energy conservation and our numerics suggests it does not occur for a time-independent Hamiltonian.