A rigorous theory of many-body prethermalization for periodically driven and closed quantum systems

DOI10.1007/S00220-017-2930-XzbMATH Open1370.81226arXiv1509.05386OpenAlexW3104756137MaRDI QIDQ2014266

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Publication date: 10 August 2017

Published in: (Search for Journal in Brave)

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 $u$. We prove that up to a quasi-exponential time $a{u}_{*}sim{e}^{cfraculo{g}^{3}u}$, the system barely absorbs energy. Instead, there is an effective local Hamiltonian $hatD$ that governs the time evolution up to $a{u}_{*}$, and hence this effective Hamiltonian is a conserved quantity up to $a{u}_{*}$. 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 $a{u}_{*}$ that is (almost) exponential in $U/J$.

Full work available at URL: https://arxiv.org/abs/1509.05386

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