Robust extended states in Anderson model on partially disordered random regular graphs

Author:

Daniil Kochergin, Ivan M. Khaymovich, Olga Valba, Alexander Gorsky

Keyword:

Condensed Matter, Disordered Systems and Neural Networks, Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistical Mechanics (cond-mat.stat-mech), High Energy Physics - Theory (hep-th), Quantum Physics (quant-ph)

journal:

date:

2023-09-10 16:00:00

Abstract

In this work we analytically explain the origin of the mobility edge in partially disordered ensemble of random regular graphs (RRG), with the connectivity $d$, the position of which is under control. It is shown that the mobility edge in the spectrum survives in some region in $(\beta,d)$-parameter plane at infinitely large uniformly distributed disorder, where $\beta$ stands for the fraction of %clean disordered nodes. The critical curve separating %regimes with and without mobility edge extended and localized states is derived analytically and confirmed numerically. The duality in the localization properties between the sparse and extremely dense RRG has been found and understood. The localization properties of the partially disordered RRG supplemented by the non-reciprocity parameter as well as the chemical potential for the $3$-cycles have been analyzed numerically.

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