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

We analyze the 1D Anderson model with stealthy disorder, defined by a power spectrum that vanishes over a continuous band of wavenumbers. Perturbative expansion of the self-energy and numerical results show that for small disorder $W$ and prescribed stealthiness $\chi$, the system is effectively delocalized, i.e., the localization length $\xi$ exceeds large system sizes. This unusual behavior follows from the systematic cancellation of leading terms so that $\xi$ scales as $W^{-2n}$ with large $n$. Since the underlying mechanism depends only on the stealthy disorder, our findings also apply to photonic and phononic waves.

Recommended citation: Vanoni, C., Karcher, J., Rechtsman, M. C., Altshuler, B. L., Steinhardt, P. J., and Torquato, S. (2026). "Effective delocalization in the one-dimensional Anderson model with stealthy disorder." Phys. Rev. Lett. 136, 150404.
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