Universal localization-delocalization transition in chiral-symmetric Floquet drives

Abstract

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 ($0 \le t \le \td$). We find that the time-dependent localization length $\lloc(t)$ diverges with a universal exponent as $t$ approaches the midpoint of the drive: $\lloc(t) \sim (t - \td/2)^{-ν}$ with $\hat{I}½=2$. We provide analytical and numerical evidence for the universality of this exponent within the AIII symmetry class.

18 + 8 pages, 8 figures; revised introduction, further discussion of analyticity and comparison to plateau transition, references and Appendices C and D added, minor corrections, published version