Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains

Floquet spin chains have been a venue for understanding topological states of matter that are qualitatively different from their static counterparts by, for example, hosting $\pi$ edge modes that show stable period-doubled dynamics. However the stability of these edge modes to interactions has traditionally required the system to be many-body localized in order to suppress heating. In contrast, here we show that even in the absence of disorder, and in the presence of bulk heating, $\pi$ edge modes are long lived. Their lifetime is extracted from exact diagonalization and is found to be non-perturbative in the interaction strength. A tunneling estimate for the lifetime is obtained by mapping the stroboscopic time-evolution to dynamics of a single particle in Krylov subspace. In this subspace, the $\pi$ edge mode manifests as the quasi-stable edge mode of an inhomogeneous Su-Schrieffer-Heeger model whose dimerization vanishes in the bulk of the Krylov chain.