Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

• URL: http://arxiv.org/abs/2101.07065v1
• Date: Mon, 18 Jan 2021 13:22:54 GMT
• Title: Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems
• Authors: Takashi Mori, Hongzheng Zhao, Florian Mintert, Johannes Knolle, Roderich Moessner
• Abstract summary: We derive rigorous, non-perturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasi-periodic driving. Our bound for Thue-Morse quasi-periodic driving suggests that the heating time scales like $(omega/g)-Cln(omega/g)$ with a positive constant $C$ and a typical energy scale $g$ of the Hamiltonian.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but a- and quasi-periodic driving is still limited. Here, we derive rigorous, non-perturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasi-periodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasi-periodic driving suggests that the heating time scales like $(\omega/g)^{-C\ln(\omega/g)}$ with a positive constant $C$ and a typical energy scale $g$ of the Hamiltonian, in agreement with our numerical simulations.

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