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| VOLUME 116 (2022) | ISSUE 6 | PAGE 392 |
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Mobility edge in the Anderson model on partially disordered random regular graphs
O. Valba+, A. Gorsky*×
+Department of Applied Mathematics, Tikhonov Moscow Institute of Electronics and Mathematics, National Research University Higher School of Economics, 123458 Moscow, Russia *Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051 Moscow, Russia ×Moscow Institute for Physics and Technology, 141700 Dolgoprudny, Russia
Abstract
In this Letter 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. |