TY - JOUR
T1 - Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems
AU - Kuwahara, Tomotaka
AU - Mori, Takashi
AU - Saito, Keiji
N1 - Funding Information:
We thank Yuji Shirai and Yoshihito Hotta for valuable comments on the manuscript. TK acknowledges the support from JSPS grant no. 2611111 . TM was supported by the JSPS Core-to-Core Program “Non-equilibrium dynamics of soft matter and information” and JSPS KAKENHI Grant No. 15K17718. K.S. was supported by MEXT grant no. 25103003 .
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.
AB - This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.
KW - Energy absorption
KW - Floquet-Magnus expansion
KW - Generic few-body Hamiltonian
KW - Periodically driven system
KW - Prethermalization
KW - Transient dynamics
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U2 - 10.1016/j.aop.2016.01.012
DO - 10.1016/j.aop.2016.01.012
M3 - Article
AN - SCOPUS:84958045504
SN - 0003-4916
VL - 367
SP - 96
EP - 124
JO - Annals of Physics
JF - Annals of Physics
ER -