Mobility Edge in the Anderson model on partially disordered random regular graphs

TL;DR

This study numerically identifies a sharp mobility edge in the spectrum of the Anderson model on partially disordered random regular graphs, with implications for understanding many-body localization.

Contribution

It introduces a novel numerical analysis of the Anderson model on partially disordered RRGs, revealing a mobility edge linked to the density of clean nodes.

Findings

Sharp mobility edge exists above a critical density of clean nodes.

Position of the mobility edge is nearly independent of disorder strength.

Results have implications for the debate on mobility edges in many-body localized phases.

Abstract

In this Letter we study numerically the Anderson model on partially disordered random regular graphs (RRG) 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 RRG ensemble. Using adjacent gap ratio statistics and IPR 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 (MBL) phase is discussed.