Asymptotic Prethermalization in Periodically Driven Classical Spin Chains

Owen Howell, Phillip Weinberg, Dries Sels, Anatoli Polkovnikov, and Marin Bukov

Phys. Rev. Lett. 122, 010602 – Published 9 January 2019

Abstract

We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Even though there is no straightforward generalization of Floquet’s theorem to nonlinear systems, we present strong evidence that the prethermal physics is well described by the inverse-frequency expansion. We relate the stability and robustness of the prethermal plateau to drive-induced synchronization not captured by the expansion. Our results set the pathway to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for photonic crystals and cold atom experiments in the superfluid regime.

Received 13 February 2018
Revised 17 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.010602

Physics Subject Headings (PhySH)

Cold atoms & matter waves

Atomic, Molecular & Optical

Authors & Affiliations

Owen Howell^1,*, Phillip Weinberg¹, Dries Sels^1,2,3, Anatoli Polkovnikov¹, and Marin Bukov^4,†

¹Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
²Department of Physics, Harvard University, 17 Oxford st., Cambridge, Massachusetts 02138, USA
³Theory of quantum and complex systems, Universiteit Antwerpen, B-2610 Antwerpen, Belgium
⁴Department of Physics, University of California, Berkeley, California 94720, USA