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

Dmitry Abanin, Wojciech De Roeck, Wen Wei Ho, François Huveneers

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226 Scopus citations

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 ν. We prove that up to a quasi-exponential time τ∗∼ecνlog3ν, the system barely absorbs energy. Instead, there is an effective local Hamiltonian D^ 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.

Original languageEnglish (US)
Pages (from-to)809-827
Number of pages19
JournalCommunications In Mathematical Physics
Volume354
Issue number3
DOIs
StatePublished - Sep 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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