Exponentially slow heating in short and long-range interacting Floquet systems

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Exponentially slow heating in short and long-range interacting Floquet systems

Francisco Machado, Gregory D. Kahanamoku-Meyer, Dominic V. Else, Chetan Nayak, and Norman Y. Yao

Phys. Rev. Research 1, 033202 – Published 24 December 2019

Abstract

We analyze the dynamics of periodically driven (Floquet) Hamiltonians with short and long-range interactions, finding clear evidence for a thermalization time, $τ^{*}$ , that increases exponentially with the drive frequency. Using a combination of heating and entanglement dynamics, we explicitly extract the effective energy scale controlling the rate of thermalization. Finally, we demonstrate that for times shorter than $τ^{*}$ , the dynamics of the system is well approximated by evolution under a time-independent Hamiltonian, $D_{eff}$ , for both short-range interacting systems, in agreement with recent rigorous bounds, as well as for long-range interacting systems, where such results do not exist at present.

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Received 8 September 2017
Revised 14 February 2019

DOI:https://doi.org/10.1103/PhysRevResearch.1.033202

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Floquet systems Long-range interactions Quantum control Quantum simulation Quantum statistical mechanics

Spin chains

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsAtomic, Molecular & OpticalStatistical Physics & ThermodynamicsGeneral Physics

Authors & Affiliations

Francisco Machado ¹, Gregory D. Kahanamoku-Meyer ¹, Dominic V. Else^2,3, Chetan Nayak^2,4, and Norman Y. Yao ^1,5

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Department of Physics, University of California, Santa Barbara, California 93106, USA
³Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
⁴Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA
⁵Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

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Issue

Vol. 1, Iss. 3 — December - December 2019

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