TY - JOUR

T1 - A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

AU - Abanin, Dmitry

AU - De Roeck, Wojciech

AU - Ho, Wen Wei

AU - Huveneers, François

N1 - Publisher Copyright:
© 2017, Springer-Verlag GmbH Germany.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-017-2930-x

DO - 10.1007/s00220-017-2930-x

M3 - Article

AN - SCOPUS:85021307802

SN - 0010-3616

VL - 354

SP - 809

EP - 827

JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

IS - 3

ER -