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A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
Ist Teil von
Communications in mathematical physics, 2017-09, Vol.354 (3), p.809-827
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2017
Link zum Volltext
Quelle
SpringerLink (Online service)
Beschreibungen/Notizen
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
.