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Effective delocalization in the one-dimensional Anderson model with stealthy disorder

Carlo Vanoni,Jonas Karcher,Mikael C. Rechtsman,Boris L. Altshuler,P. Steinhardt,S. Torquato

Published 2025 in Unknown venue

ABSTRACT

We study analytically and numerically the Anderson model in one dimension with"stealthy"disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical transparency properties of stealthy hyperuniform layered media, we compute the localization length using a perturbative expansion of the self-energy. We find that, for fixed energy and small but finite disorder strength $W$, there exists for any finite length system a range of stealthiness $\chi$ for which the localization length exceeds the system size. This kind of"effective delocalization"is the result of the novel kind of correlated disorder that spans a continuous range of length scales, a defining characteristic of stealthy systems. Unlike uncorrelated disorder, for which the localization length $\xi$ scales as $W^{-2}$ to leading order for small W, the leading order terms in the perturbation expansion of $\xi$ for stealthy disordered systems vanish identically for a progressively large number of terms as $\chi$ increases such that $\xi$ scales as $W^{-2n}$ with arbitrarily large $n$. Moreover, we support our analytical results with numerical simulations. Our results introduce stealthy disorder into quantum tight-binding models and show that enforcing a low-$k$ spectral gap markedly alters the scattering landscape, enabling localization lengths that exceed the system size at fixed disorder strength. Since this mechanism relies only on the spectral properties of the disorder, it carries over directly to photonic and phononic wave systems.

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