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

• Published in: Communications in mathematical physics 2017-09, Vol.354 (3), p.809-827
• Main Authors: Abanin, Dmitry, De Roeck, Wojciech, Ho, Wen Wei, Huveneers, François
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Complex Systems; Energy absorption; Evolution; Mathematical and Computational Physics; Mathematical Physics; Mathematics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Separation; Theoretical
• ISSN: 0010-3616; 1432-0916
• DOI: 10.1007/s00220-017-2930-x

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 ∗ ∼ e c ν log 3 ν , 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 .