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

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.

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• Role of Fock-space correlations in many-body localization
• Ergodicity-to-localization transition on random regular graphs with large connectivity and in many-body quantum dots
• Anatomy of the fragmented Hilbert space: eigenvalue tunneling, quantum scars and localization in the perturbed random regular graph
• Robust extended states in Anderson model on partially disordered random regular graphs
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space