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

TL;DR

This paper demonstrates that $$ edge modes in disorder-free Floquet spin chains are long-lived despite bulk heating, with their lifetime being non-perturbative in interaction strength, challenging the need for many-body localization.

Contribution

It shows that $$ edge modes can be stable in disorder-free, interacting Floquet systems with bulk heating, and provides a tunneling estimate for their lifetime.

Findings

$$ edge modes are long-lived without disorder.

Lifetime is non-perturbative in interaction strength.

Edge mode behavior maps to an inhomogeneous Su-Schrieffer-Heeger model.

Abstract

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.