Fixed points of Wegner-Wilson flows and many-body localization

Understand

Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization.

• Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself.
• We formulate a robust algorithm, based on Wegner Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions.
• We present evidence for the existence of distinct fixed point distributions of the latter: a flat "white noise" distribution in the ergodic phase, a "1/f" law inside the MBL phase, and scale-free distributions in the transition regime.