期刊
COMMUNICATIONS IN MATHEMATICAL PHYSICS
卷 354, 期 3, 页码 809-827出版社
SPRINGER
DOI: 10.1007/s00220-017-2930-x
关键词
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资金
- Alfred Sloan Foundation
- Deutsche Forschungsgesellschaft, DFG [RO 4522/1-1]
- Belgian Interuniversity Attraction Pole [P07/18 Dygest]
- ANR
- CNRS InPhyNiTi Grant (MaBoLo)
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 . We prove that up to a quasi-exponential time , the system barely absorbs energy. Instead, there is an effective local Hamiltonian that governs the time evolution up to , and hence this effective Hamiltonian is a conserved quantity up to . 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 that is (almost) exponential in U/J.
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