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

Dmitry Abanin; Wojciech De Roeck; Wen Wei Ho; Francois Huveneers

doi:10.1007/s00220-017-2930-x

paper

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

arXiv:1509.05386 · doi:10.1007/s00220-017-2930-x

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 $τ_{*} \sim e^{c \frac{ν}{l o g ^{3} ν}}$ , 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 $U / J$ .

21 pages, file updated to match published version

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

Abstract

References in corpus (12)

Cited by in corpus (252)