Anderson localisation on spatially structured random graphs shows a transition shifting to stronger disorder with increasing hopping range, vanishing beyond a critical range with direct delocalised-localised transition and Kosterlitz-Thouless-like scaling, without an intervening multifractal phase.
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Stealthy disorder in the 1D Anderson model makes the localization length scale as a higher inverse power of disorder strength W, allowing it to exceed system size for sufficient stealthiness parameter χ.
A flow equation for the resonance density exponent θ(w) derived in the SJA predicts resonance proliferation driving delocalization, with θ(w)>0 for localized phases and instability signaling thermalization, matching numerics in Anderson and MBL models.
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Effective delocalization in the one-dimensional Anderson model with stealthy disorder
Stealthy disorder in the 1D Anderson model makes the localization length scale as a higher inverse power of disorder strength W, allowing it to exceed system size for sufficient stealthiness parameter χ.