The transition between ergodic and many-body localized (MBL) phases is expected to occur via an avalanche mechanism, in which ergodic bubbles that arise due to local fluctuations in system properties thermalize their surroundings leading to delocalization of the system, unless the disorder is sufficiently strong to stop this process. We propose an algorithm based on neural networks that allows us to detect the ergodic bubbles using experimentally measurable two-site correlation functions. Investigating the time evolution of the system, we observe a logarithmic in time growth of the ergodic bubbles in the MBL regime. The distribution of the size of ergodic bubbles converges during time evolution to an exponentially decaying distribution in the MBL regime, and a power-law distribution with a thermal peak in the critical regime, supporting thus the scenario of delocalization through the avalanche mechanism. Our algorithm permits us to pinpoint the quantitative differences in the time evolution of systems with random and quasiperiodic potentials, as well as to identify rare (Griffiths) events. Our results open different pathways in studies of the mechanisms of thermalization of disordered many-body systems and beyond.

• Received 9 June 2021
• Revised 14 October 2021
• Accepted 15 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L140202