Analytic approaches to periodically driven closed quantum systems: Methods and Applications

Abstract

We present a brief overview of some of the analytic perturbative techniques for the computation of the Floquet Hamiltonian for a periodically driven, or Floquet, quantum many-body system. The key technical points about each of the methods discussed are presented in a pedagogical manner. They are followed by a brief account of some chosen phenomena where these methods have provided useful insights. We provide an extensive discussion of the Floquet-Magnus expansion, the adiabatic-impulse approximation, and the Floquet perturbation theory. This is followed by a relatively short discourse on the rotating wave approximation, a Floquet-Magnus resummation technique and the Hamiltonian flow method. We also provide a discussion of some open problems which may possibly be addressed using these methods.

arXiv commentv2; Minor changes and more refs added

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Cited by in corpus (40)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Minimal model for Hilbert space fragmentation with local constraints
• Non-Hermitian Floquet Topological Matter -- A Review
• Dynamical relaxation of correlators in periodically driven integrable quantum systems
• Prethermal fragmentation in a periodically driven Fermionic chain
• Generation of higher-order topological insulators using periodic driving
• Periodically driven Rydberg chains with staggered detuning
• Out-of-Time-Order correlators in driven conformal field theories
• Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Signatures of multifractality in a periodically driven interacting Aubry-André model
• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Hinge mode dynamics of periodically driven higher-order Weyl semimetals
• Dynamical localization and slow thermalization in a class of disorder-free periodically driven one-dimensional interacting systems
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Exactly Solvable Floquet Dynamics for Conformal Field Theories in Dimensions Greater than Two
• Dynamical Freezing in Exactly Solvable Models of Driven Chaotic Quantum Dots
• Driven Hubbard model on a triangular lattice: tunable Heisenberg antiferromagnet with three-spin chiral term
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Floquet Engineering of Hilbert Space Fragmentation in Stark Lattices
• Sharp detection of the onset of Floquet heating using eigenstate sensitivity
• Disconnected entanglement entropy as a marker of edge modes in a periodically driven Kitaev chain
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• Signatures of fragmentation for periodically driven fermions
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• Arresting Quantum Chaos Dynamically in Transmon Arrays
• Dynamical freezing and switching in periodically driven bilayer graphene
• Discrete Time Crystal Phase of Higher Dimensional Integrable Models
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• Real space thermalization of locally driven quantum magnets
• Detecting prethermal Floquet phases of Rydberg atom arrays
• Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Characterizing the transition from topology to chaos in a kicked quantum system
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