Short talk at the 129th Statistical Mechanics Conference
Date:
Title: Effective delocalization in the one-dimensional Anderson model with stealthy disorder
Abstract: We investigate analytically and numerically the one-dimensional Anderson model with stealthy disorder, characterized by a power spectrum that vanishes over a continuous range of wave numbers. Motivated by recent studies on the optical transparency of stealthy hyperuniform layered media, we calculate the localization length using a perturbative expansion of the self-energy. For fixed energy and small but finite disorder strength $W$, we show that there exists, for any finite system size, a range of stealthiness $\chi$ where the localization length exceeds the system length, leading to an “effective delocalization.” This phenomenon arises from the long-range correlations inherent to stealthy disorder, which suppress contributions across a continuous range of length scales. Unlike uncorrelated disorder, where the localization length $\xi \sim W^{-2}$ at leading order, in stealthy systems the first several terms of the perturbation expansion vanish as $\chi$ increases, yielding scaling of the form $\xi \sim W^{-2n}$ with arbitrarily large $n$. These analytical predictions are supported by numerical simulations. Our findings highlight the distinctive localization properties of stealthy disorder and provide a framework for exploring its implications in quantum systems of both theoretical and experimental interest.