Looking inside the avalanche in a many-body localization model

Many-body localized (MBL) systems fail to reach thermal equilibrium under their own dynamics, even though they are interacting, non-integrable, and in a highly-excited state. One instability of MBL systems is the so-called ``avalanche'', where a locally thermalizing region is able to spread thermalization through the full system. The avalanche may be modeled and numerically studied in finite one-dimensional systems by weakly coupling an infinite-temperature bath to one end of the system. We find that the avalanche spreads primarily via rare ``bottleneck" eigenstates of the closed system. These rare eigenstates are involved in exceptionally strong many-body resonances that are put ``on shell" by the bath. Thus we find and explore a detailed connection between many-body resonances and avalanches in MBL.