Mobility Edge in the Anderson Model on Partially Disordered Random Regular Graphs

Abstract

We study numerically the Anderson model on partially disordered random regular graphs considered as the toy model for a Hilbert space of interacting disordered many-body system. The protected subsector of zero-energy states in a many-body system corresponds to clean nodes in random regular graphs ensemble. Using adjacent gap ratio statistics and inverse participation ratio we find the sharp mobility edge in the spectrum of one-particle Anderson model above some critical density of clean nodes. Its position in the spectrum is almost independent on the disorder strength. The possible application of our result for the controversial issue of mobility edge in the many-body localized phase is discussed.