Kosterlitz-Thouless scaling at many-body delocalization phase transitions

We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that the transition proceeds via a `quantum avalanche'. The critical properties are captured at a coarse-grained level by a Kosterlitz-Thouless renormalization group flow. Based on this scaling picture, there are different scenarios for the behavior of fractal rare thermal inclusions within the MBL phase. We propose that the near-critical MBL phase could host rare thermal regions that are power-law distributed in size. This points to the existence of a second transition within the MBL phase, at which these power-laws change to a stretched exponential form. Large scale numerical simulations of a phenomenological models capturing the critical properties near the MBL transition support this picture.