Universal localization-delocalization transition in chiral-symmetric Floquet drives

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 ($0\le t\le \text{td}$). We find that the time-dependent localization length $\text{lloc}(t)$ diverges with a universal exponent as $t$ approaches the midpoint of the drive: $\text{lloc}(t)\sim (t-\text{td}\mathrm{/}2{)}^{-\nu }$ with $\nu =2$. We provide analytical and numerical evidence for the universality of this exponent within the AIII symmetry class.