Quasiperiodicity hinders ergodic Floquet eigenstates

TL;DR

This paper demonstrates that quasiperiodic driving in one-dimensional systems prevents ergodic and thermalizing behavior, with all Floquet eigenstates remaining non-ergodic in the thermodynamic limit, challenging previous expectations.

Contribution

It reveals that quasiperiodicity hinders ergodicity in driven systems, showing all Floquet eigenstates are non-ergodic regardless of system size or driving parameters.

Findings

Non-ergodic Floquet states persist at the thermodynamic limit.

Scaling the quenching period with system size can recover ergodicity.

All Floquet eigenstates are either localized or ballistic, not ergodic.

Abstract

Quasiperiodic systems in one dimension can host non-ergodic states, e.g. localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e. spatially localized or ballistic. However, periodic quenches across these two non-ergodic phases were thought to produce ergodic diffusive-like states even for non-interacting particles. We show that this expectation is not met at the thermodynamic limit where the system always attains a non-ergodic state. We find that ergodicity may be recovered by scaling the Floquet quenching period with system size and determine the corresponding scaling function. Our results suggest that while the fraction of spatially localized or ballistic states depends on the model's details, all Floquet eigenstates belong to one of these non-ergodic categories. Our findings demonstrate that quasiperiodicity hinders ergodicity and thermalization, even in driven systems where these phenomena are commonly expected.