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Title: Periodically driven ergodic and many-body localized quantum systems

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Publication Date:
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE), Fuel Cycle Technologies (NE-5)
OSTI Identifier:
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Annals of Physics
Additional Journal Information:
Journal Volume: 353; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-05-05 03:01:43; Journal ID: ISSN 0003-4916
Country of Publication:
United States

Citation Formats

Ponte, Pedro, Chandran, Anushya, Papić, Z., and Abanin, Dmitry A. Periodically driven ergodic and many-body localized quantum systems. United States: N. p., 2015. Web. doi:10.1016/j.aop.2014.11.008.
Ponte, Pedro, Chandran, Anushya, Papić, Z., & Abanin, Dmitry A. Periodically driven ergodic and many-body localized quantum systems. United States. doi:10.1016/j.aop.2014.11.008.
Ponte, Pedro, Chandran, Anushya, Papić, Z., and Abanin, Dmitry A. 2015. "Periodically driven ergodic and many-body localized quantum systems". United States. doi:10.1016/j.aop.2014.11.008.
title = {Periodically driven ergodic and many-body localized quantum systems},
author = {Ponte, Pedro and Chandran, Anushya and Papić, Z. and Abanin, Dmitry A.},
abstractNote = {},
doi = {10.1016/j.aop.2014.11.008},
journal = {Annals of Physics},
number = C,
volume = 353,
place = {United States},
year = 2015,
month = 2

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.aop.2014.11.008

Citation Metrics:
Cited by: 105works
Citation information provided by
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  • We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disorderedmore » spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.« less
  • This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian onmore » the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.« less
  • According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classicalmore » (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space. -- Highlights: •A dynamical localization transition in periodically driven ergodic systems is found. •This phenomenon is reminiscent of many-body localization in energy space. •Our results are valid for classical and quantum systems in the thermodynamic limit. •At critical frequency, the short time expansion for the evolution operator breaks down. •The transition is associated to a divergent time scale.« less
  • We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. Inmore » all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.« less