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

TL;DR

This paper analytically explains the origin and conditions of the mobility edge in partially disordered random regular graphs, revealing a critical curve and duality in localization properties, supported by numerical confirmation.

Contribution

It provides an analytical derivation of the mobility edge and the critical parameters in partially disordered RRGs, enhancing understanding of localization transitions.

Findings

Mobility edge persists in certain parameter ranges at high disorder.

Derived an analytical critical curve separating extended and localized states.

Discovered a duality in localization properties between sparse and dense RRGs.

Abstract

In this work we analytically explain the origin of the mobility edge in the partially disordered random regular graphs of degree d, i.e., with a fraction $\beta$ of the sites being disordered, while the rest remain clean. It is shown that the mobility edge in the spectrum survives in {a certain range of parameters} $(d,\beta)$ at infinitely large uniformly distributed disorder. The critical curve separating 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.