Glassy properties of Anderson localization: pinning, avalanches and chaos

Abstract

I present the results of extensive numerical simulations which reveal the glassy properties of Anderson localization in dimension two at zero temperature: pinning, avalanches and chaos. I first show that strong localization confines quantum transport along paths which are pinned by disorder but can change abruptly and suddenly (avalanches) when the energy is varied. I determine the roughness exponent $\zeta$ characterizing the transverse fluctuations of these paths and find that its value $\zeta =2/3$ is the same as for the directed polymer problem. Finally, I characterize the chaos property, namely the fragility of the conductance with respect to small perturbations in the disorder configuration. It is linked to interference effects and universal conductance fluctuations at weak disorder, and more spin-glass-like behavior at strong disorder.

arXiv comment6 + 5 (supplemental material) pages, 4 + 6 figures. Corresponds to the published version

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• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
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• 2D Anderson Localization and KPZ sub-Universality Classes : sensitivity to boundary conditions and insensitivity to symmetry classes