Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems

By Tomotaka Kuwahara, Takashi Mori, Keiji Saito. 2015

409 citations recorded by the source corpus.

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 after infinite-time evolution, irrespective of dynamical details. In the present study, instead of considering infinitely long-time scale, we aim to provide a framework to understand the long but finite time behavior, namely the transient dynamics. In the 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 finite-time scale. Our result reveals a reliable time scale of the validity of the FM expansion, which can be comparable to the experimental time scale. Furthermore, 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 generic scenario of the prethermalization phenomenon in periodically driven systems.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/1a75189e15658152b8cddff9918a53010e1ed5f5

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems (2015, background): “In the case where the driving is localized (as opposed to ‘a sum of local terms’), [24] contains a much stronger result, namely that the one-cycle unitary of the process is close in operator norm to the unitary generated by an effective Hamiltonian.”
Colloquium: Nonthermal pathways to ultrafast control in quantum materials (2021, background): “In this limit rigorous results for slow heating were recently established (Abanin, De Roeck, and Huveneers, 2015; Kuwahara, Mori, and Saito, 2016; Mori, Kuwahara, and Saito, 2016; Abanin et al., 2017a, 2017b; Ho, Protopopov, and Abanin, 2018; Mori et al., 2018).”
Prethermalization and Thermalization in Isolated Quantum Systems (2018, background): “In general, they quickly reach a time-periodic state that can be identified as a Gibbs state corresponding to an effective Hamiltonian, before relaxing to the thermal (infinite-temperature [26, 27]) state in a timescale that is exponentially long in the frequency of the drive [28–33].”
QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains (2016, background): “Since heating can be exponentially slow at high frequencies [46, 47, 48, 49], one might be interested in calculating also the infinite-time quantities”