Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

Qin, Tao; Hofstetter, Walter

doi:10.1103/physrevb.96.075134

Cited by 19 publications

(11 citation statements)

References 46 publications

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“…Another promising application of our scheme is its use within the Floquet-implementation of DMFT [72][73][74][75][76], which directly treats the nonequilibrium steady state of periodically driven systems. These calculations include a coupling to a heat bath and interesting applications such as the high-harmonic generation in solids [77] involve the simulation of highly excited nonequilibrium states.…”

Section: Discussionmentioning

confidence: 99%

Truncating the memory time in nonequilibrium dynamical mean field theory calculations

Schüler¹,

Eckstein²,

Werner³

2018

Phys. Rev. B

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The nonequilibrium Green's functions (NEGF) approach is a versatile theoretical tool, which allows to describe the electronic structure, spectroscopy and dynamics of strongly correlated systems. The applicability of this method is, however, limited by its considerable computational cost. Due to the treatment of the full two-time dependence of the NEGF the underlying equations of motion involve a long-lasting non-Markovian memory kernel that results in at least a 3 scaling in the number of time points . The system's memory time is, however, reduced in the presence of a thermalizing bath. In particular, dynamical mean-field theory (DMFT) -one of the most successful approaches to strongly correlated lattice systems -maps extended systems to an effective impurity coupled to a bath. In this work, we systematically investigate how the memory time can be truncated in nonequilibrium DMFT simulations of the Hubbard and Hubbard-Holstein model. We show that suitable truncation schemes, which substantially reduce the computational cost, result in excellent approximations to the full time evolution. This approach enables the propagation to longer times, making fundamental processes like prethermalization and the final stages of thermalization accessible to nonequilibrium DMFT.

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Section: Discussionmentioning

confidence: 99%

Truncating the memory time in nonequilibrium dynamical mean field theory calculations

Schüler¹,

Eckstein²,

Werner³

2018

Phys. Rev. B

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“…The role of interactions in non-equilibrium driven systems is much more subtle. While interactions may allow for interesting correlations to build up [12,[40][41][42][43][44][45][46][47][48][49], they also provide pathways for the system to absorb energy from the driving field, and thereby to heat up [50][51][52][53]. Thus understanding the interplay between these phenomena and the parameters that control them is crucial for enabling further advances in the field.…”

mentioning

confidence: 99%

Many-Body Dynamics and Gap Opening in Interacting Periodically Driven Systems

Kandelaki¹,

Rudner²

2018

Phys. Rev. Lett.

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We study transient dynamics in a two-dimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. We investigate the dynamics of this gap opening process, taking into account the essential role of electron-electron interactions. Crucially, scattering due to interactions (1) induces dephasing, which erases memory of the system's prequench state and yields the intrinsic timescale for gap emergence, and (2) provides a mechanism for the system to absorb energy of the drive, leading to heating which must be mitigated to ensure the success of Floquet band engineering. We characterize the gap opening process via the system's generalized spectral function and correlators probed by photoemission experiments, and we identify a parameter regime at moderate driving frequencies where a hierarchy of timescales allows a well-defined Floquet gap to be produced and studied before the deleterious effects of heating set in.

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“…Nonetheless, analogous spectral information to that familiar from equilibrium systems can be obtained for Floquet systems (see Refs. [8,9,[71][72][73][74]), provided that the system is noninteracting and/or that it is in a time-periodic steady state. Under these conditions, G R (t, t ) is periodic in the average (or "center of mass") time t = 1 2 (t + t ) with period T : shifting both t and t by T leaves the state of the system invariant.…”

Section: B Properties Of the Floquet Retarded Green's Functionmentioning

confidence: 99%

The Floquet Engineer's Handbook

Rudner,

Lindner

2020

Preprint

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We provide a pedagogical technical guide to many of the key theoretical tools and ideas that underlie work in the field of Floquet engineering. We hope that this document will serve as a useful resource for new researchers aiming to enter the field, as well as experienced researchers who wish to gain new insight into familiar or possibly unfamiliar methods. This guide was developed out of supplementary material as a companion to our recent review, "Band structure engineering and non-equilibrium dynamics in Floquet topological insulators," arXiv:1909.02008 (2019. The primary focus is on analytical techniques relevant for Floquet-Bloch band engineering and related many-body dynamics. We will continue to update this document over time to include additional content, and welcome suggestions for further topics to consider. CONTENTS I. Introduction 1 II. Floquet theory basics and formalism 2 A. Frequency-space formulation 2 B. Truncation of frequency space 4 C. Floquet Fermi's golden rule 5 III. Gap opening due to circularly polarized driving fields 9 IV. Vanishing of the winding number ν 1 for continuous time evolution 9 V. Definition of the time-averaged spectral function 9 A. Formal definitions 10 B. Properties of the Floquet retarded Green's function 10 C. Evaluation of the Floquet retarded Green's function for a non-interacting system 11 VI. Floquet-Kubo formula 12 A. Floquet-Kubo Formula for the electrical conductivity 13 VII. Acknowledgements 15 References 15

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Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study

Cited by 19 publications

References 46 publications

Truncating the memory time in nonequilibrium dynamical mean field theory calculations

Truncating the memory time in nonequilibrium dynamical mean field theory calculations

Many-Body Dynamics and Gap Opening in Interacting Periodically Driven Systems

The Floquet Engineer's Handbook

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