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arXiv:2302.12271 · Physical review. B./Physical review. B

Dynamical localization and slow dynamics in quasiperiodically driven quantum systems

Vatsana Tiwari, Devendra Singh Bhakuni, Auditya Sharma

Published Apr 3, 2024• 21 citations
arXivHTMLPDF

Abstract

We investigate the role of a quasiperiodically driven electric field in a disordered fermionic chain. In the clean noninteracting case, we show the emergence of dynamical localization---a phenomenon previously known to exist only for a perfect periodic drive. In contrast, in the presence of disorder, where a high-frequency periodic drive preserves Anderson localization, we show that the quasiperiodic drive destroys it and leads to slow relaxation. Considering the role of interactions, we uncover the phenomenon of quasiperiodic driving-induced logarithmic relaxation, where a suitably tuned drive (corresponding to dynamical localization in the clean, noninteracting limit) slows down the dynamics even when the disorder is small enough for the system to be in the ergodic phase. This is in sharp contrast to the fast relaxation seen in the undriven model, as well as the absence of thermalization (drive-induced many-body localization) exhibited by a high-frequency periodic drive.

DOI
10.1103/physrevb.109.l161104

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We investigate the role of a quasiperiodically driven electric field in a disordered fermionic chain. In the clean noninteracting case, we show the emergence of dynamical localization---a phenomenon previously known to exist only for a perfect periodic drive. In contrast, in the presence of disorder, where a high-frequency periodic drive preserves Anderson localization, we show that the quasiperiodic drive destroys it and leads to slow relaxation. Considering the role of interactions, we uncover the phenomenon of quasiperiodic driving-induced logarithmic relaxation, where a suitably tuned drive (corresponding to dynamical localization in the clean, noninteracting limit) slows down the dynamics even when the disorder is small enough for the system to be in the ergodic phase. This is in sharp contrast to the fast relaxation seen in the undriven model, as well as the absence of thermalization (drive-induced many-body localization) exhibited by a high-frequency periodic drive.
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We study if the interplay between dynamical localization and interactions in periodically driven quantum systems can give rise to anomalous thermalization behavior. Specifically, we consider one-dimensional models with interacting spinless fermions with nearest-neighbor hopping and density-density interactions, and a periodically driven on-site potential with spatial periodicity m=2 and m=4. At a dynamical localization point, these models evade thermalization either due to the presence of an extensive number of conserved quantities (for weak interactions) or due to the kinetic constraints caused by drive-induced resonances (for strong interactions). Our models therefore illustrate interesting mechanisms for generating constrained dynamics in Floquet systems which are difficult to realize in an undriven system.
We study the combined effect of quasiperiodic disorder, driven, and interaction in the periodically kicked Aubry-Andr\'e model. In the noninteracting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from the ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for the strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-Andr\'e model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.
Recently it has been shown that interparticle interactions generically destroy dynamical localization in periodically driven systems, resulting in diffusive transport and heating. In this Rapid Communication we rigorously construct a family of interacting driven systems which are dynamically localized and effectively decoupled from the external driving potential. We show that these systems exhibit tunable periodic or quasiperiodic revivals of the many-body wave function and thus of all physical observables. By numerically examining spinless fermions on a one-dimensional lattice we show that the analytically obtained revivals of such systems remain stable for finite systems with open boundary conditions while having a finite lifetime in the presence of static spatial disorder. We find this lifetime to be inversely proportional to the disorder strength.