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In this Letter we study numerically the Anderson model on partiallydisordered random regular graphs (RRG) considered as the toy model for aHilbert space of interacting disordered many-body system. The protectedsubsector of zero-energy states in a many-body system corresponds to cleannodes in RRG ensemble. Using adjacent gap ratio statistics and IPR we find thesharp mobility edge in the spectrum of one-particle Anderson model above somecritical density of clean nodes. Its position in the spectrum is almostindependent on the disorder strength. The possible application of our resultfor the controversial issue of mobility edge in the many-body localized (MBL)phase is discussed.

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