Periodically driven systems often exhibit behavior distinct from static systems. In single-particle, static systems, any amount of disorder generically localizes all eigenstates in one dimension. In contrast, we show that in topologically nontrivial, single-particle Floquet loop drives with chiral symmetry in one dimension, a localization-delocalization transition occurs as the time $t$ is varied within the driving period ($0\le t\le T_{\text{drive}}$). We find that the time-dependent localization length $L_{\mathrm{loc}}\left(t\right)$ diverges with a universal exponent as $t$ approaches the midpoint of the drive: $L_{\mathrm{loc}}\left(t\right)\sim {(t-T_{\text{drive}}/2)}^{-\nu }$ with $\nu =2$. We provide analytical and numerical evidence for the universality of this exponent within the AIII symmetry class.

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• Anderson localization
• Quantum walks
• Disordered systems
• Floquet systems
• Topology