A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
By D. Abanin, Wojciech De Roeck, Wen Wei Ho, F. Huveneers. 2015
344 citations recorded by the source corpus.
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 $${\nu}$$ν. We prove that up to a quasi-exponential time $${\tau_* \sim {\rm e}^{c \frac{\nu}{\log^3 \nu}}}$$τ∗∼ecνlog3ν, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $${\widehat D}$$D^ that governs the time evolution up to $${\tau_*}$$τ∗, and hence this effective Hamiltonian is a conserved quantity up to $${\tau_*}$$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 $${\tau_*}$$τ∗ that is (almost) exponential in $${U/J}$$U/J.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/a70067542fc909ebe6b94d69a4c32b0c413ee17e
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Citations in the corpus
- A Universal Operator Growth Hypothesis (2018, background): “[35] Dmitry Abanin, Wojciech De Roeck, Wen Wei Ho, and”
- Pre-thermal phases of matter protected by time-translation symmetry (2016, background): “[75] Dmitry Abanin, Wojciech De Roeck, Francois Huveneers, and Wen Wei Ho, “A rigorous theory of manybody prethermalization for periodically driven and closed quantum systems,” (2015), arXiv:1509.”
- Colloquium: Atomic quantum gases in periodically driven optical lattices (2016, background): “…local state space, e.g. fermionic Hubbard or spin models, it was shown very recently that th increases exponentially with the driving frequency (Abanin et al., 2015c; Kuwahara et al., 2016; Mori et al., 2016) and that the Floquet-Magnus expansion (18) provides at least an asymptotic expansion…”
- Probing many-body dynamics on a 51-atom quantum simulator (2017, background): “The addition of longrange interactions leads to a faster decay of the oscillations, with a timescale that is determined by 1/Vi,i+2, in good agreement with experimental observations (Fig.”
- Prethermalization and Thermalization in Isolated Quantum Systems (2018, background): “In general, they quickly reach a time-periodic state that can be identified as a Gibbs state corresponding to an effective Hamiltonian, before relaxing to the thermal (infinite-temperature [26, 27]) state in a timescale that is exponentially long in the frequency of the drive [28–33].”
- Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “In this limit rigorous results for slow heating were recently established (Abanin, De Roeck, and Huveneers, 2015; Kuwahara, Mori, and Saito, 2016; Mori, Kuwahara, and Saito, 2016; Abanin et al., 2017a, 2017b; Ho, Protopopov, and Abanin, 2018; Mori et al., 2018).”
- Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “Equivalently, such systems can be viewed as possessing an emergent prethermal conservation of dipole moment that disappears after an exponentially long timescale (113, 114, 101).”