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A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Abanin, Dmitry A.; De Roeck, Wojciech; Ho, Wen Wei; Huveneers, François (2017), A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems, Communications in Mathematical Physics, 354, 3, p. 809 - 827. 10.1007/s00220-017-2930-x

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
Communications in Mathematical Physics
Volume
354
Number
3
Publisher
Springer
Pages
809 - 827
Publication identifier
10.1007/s00220-017-2930-x
Metadata
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Author(s)
Abanin, Dmitry A.
Department of Theoretical Physics [DTP GENEVA]
De Roeck, Wojciech
Katholieke Universiteit Leuven
Institut für Theoretische Physik
Ho, Wen Wei
Department of Theoretical Physics [DTP GENEVA]
Huveneers, François
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency ν. We prove that up to a quasi-exponential time τ∗∼ecνlog3ν, the system barely absorbs energy. Instead, there is an effective local Hamiltonian Dˆ that governs the time evolution up to τ∗, and hence this effective Hamiltonian is a conserved quantity up to τ∗. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi–Hubbard model where the interaction U is much larger than the hopping J. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time τ∗ that is (almost) exponential in U/J.
Subjects / Keywords
Prethermalization; Quantum Systems

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