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arXiv:1607.07868 · Nature Physics

Periodically driving a many-body localized quantum system

Pranjal Bordia, Henrik P. Lüschen, Ulrich Schneider, Michael Knap, Immanuel Bloch

Published Jan 30, 2017• 318 citations
arXivHTMLPDF
DOI
10.1038/nphys4020

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We investigate the fate of a many-body localized phase in a non-Hermitian quasiperiodic model of hardcore bosons subjected to periodic driving. While in general, the many-body localized system is known to thermalize with increasing driving period due to Floquet heating, in this case, we demonstrate that the initially localized system first delocalizes and then localizes again, resulting in a re-entrant many-body localization (MBL) transition as a function of the driving period. Strikingly, further increase in the driving period results in a series of localization-delocalization transitions leaving behind traces of extended regimes (islands) in between MBL phases. Furthermore, non-Hermiticity renders the extended islands boundary-sensitive, resulting in a Floquet many-body skin effect under open boundaries. We present numerical evidence from spectral and dynamic studies, confirming these findings. Our study opens new pathways for understanding the interplay between non-Hermiticity and quasiperiodicity in driven systems.
We study many-body localized quantum systems subject to periodic driving. We find that the presence of a mobility edge anywhere in the spectrum is enough to lead to delocalization for any driving strength and frequency. By contrast, for a fully localized many-body system, a delocalization transition occurs at a finite driving frequency. We present numerical studies on a system of interacting one-dimensional bosons and the quantum random energy model, as well as simple physical pictures accounting for those results.
Dynamical many-body freezing occurs in periodic transverse field-driven integrable quantum spin systems. Under freezing conditions, quantum dynamics causes practically infinite hysteresis in the drive response, maintaining its starting value. We find similar resonant freezing in the Lipkin-Meshkov-Glick (LMG) model. In the LMG, the freezing conditions in the driving field suppresses the heating postulated by the eigenstate thermalization hypothesis (ETH) by inducing dynamical many-body localization, or DMBL. This is in contrast to many-body localization (MBL), which requires disorder to suppress ETH. DMBL has been validated by the inverse participation ratio (IPR) of the quasistationary Floquet modes. Similarly to the TFIM, the LMG exhibits high-frequency localization only at freezing points. IPR localization in the LMG deteriorates with an inverse system size law at lower frequencies, which indicates heating to infinite temperature. Furthermore, adiabatically increasing frequency and amplitude from low values raises the Floquet state IPR in the LMG from nearly zero to unity, indicating a phase crossover. This occurrence enables a future technique to construct an MBL engine in clean systems that can be cycled by adjusting drive parameters only.