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Anderson localization on random regular graphs (RRG) attracts much attention in view of its relation to many-body localization. Here, the authors study the statistics of eigenfunctions and energy levels on RRG, focussing on the delocalized (ergodic) phase and the critical regime. Results of exact diagonalization are in outstanding agreement with analytical theory based on the saddle-point analysis of the effective supersymmetric action supplemented by numerical solution of the corresponding self-consistency equation.
Tikhonov et al. (Mon,) studied this question.
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