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 \({\tau_* \sim {\rm e}^{c \frac{\nu}{\log^3 \nu}}}\), the system barely absorbs energy. Instead, there is an effective local Hamiltonian \({\widehat D}\) 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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Abanin, D., De Roeck, W., Ho, W.W. et al. A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems. Commun. Math. Phys. 354, 809–827 (2017). https://doi.org/10.1007/s00220-017-2930-x
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DOI: https://doi.org/10.1007/s00220-017-2930-x