Multiscale entanglement clusters at the many-body localization phase transition

Abstract

The authors construct an efficient algorithm for extracting the entanglement structure of wave functions in the form of a cluster decomposition. They apply this to the many-body localization problem by analyzing entanglement clusters in exact eigenstates. Strongly entangled ergodic clusters are connected. Their size is distributed according to a power law at the transition, while at higher disorder the distribution is a stretched exponential. This constrains possible phenomenological renormalization group descriptions of the transition, and is consistent with a Kosterlitz-Thouless type scaling.