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arXiv · 1509.05386

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

Dmitry Abanin·Wojciech De Roeck·Wen Wei Ho·Francois Huveneers
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Abstract

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 $\nu$. We prove that up to a quasi-exponential time $\tau_* \sim e^{c \frac{\nu}{\log^3 \nu}}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $\hat D$ that governs the time evolution up to $\tau_*$, and hence this effective Hamiltonian is a conserved quantity up to $\tau_*$. 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 $\tau_*$ that is (almost) exponential in $U/J$.

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Dmitry Abanin, Wojciech De Roeck, Wen Wei Ho, Francois Huveneers. 2015-09-17. A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. https://doi.org/10.1007/s00220-017-2930-x

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