Many-Body Localization with Quasiperiodic Driving

TL;DR

This paper investigates the stability of many-body localization under quasiperiodic driving, finding that MBL persists for two tones but not for three or more, and explores implications for topological order.

Contribution

It demonstrates that MBL is stable with two-tone quasiperiodic driving but destabilizes with three or more tones, extending the eigenstate thermalization hypothesis to this setting.

Findings

MBL exists for two-tone quasiperiodic driving but not for three or more tones.

Two-tone driving can host new topological orders with edge signatures.

Numerical verification supports the generalized eigenstate thermalization hypothesis.

Abstract

Sufficient disorder is believed to localize static and periodically-driven interacting chains. With quasiperiodic driving by $D$ incommensurate tones, the fate of this many-body localization (MBL) is unknown. We argue that randomly disordered MBL exists for $D=2$, but not for $D\geq 3$. Specifically, a putative two-tone driven MBL chain is neither destabilized by thermal avalanches seeded by rare thermal regions, nor by the proliferation of long-range many-body resonances. For $D\geq 3$, however, sufficiently large thermal regions have continuous local spectra and slowly thermalize the entire chain. En route, we generalize the eigenstate thermalization hypothesis to the quasiperiodically-driven setting, and verify its predictions numerically. Two-tone driving enables new topological orders with edge signatures; our results suggest that localization protects these orders indefinitely.