Replica resummation of the Baker-Campbell-Hausdorff series

Abstract

We developed a novel perturbative expansion based on the replica trick for the Floquet Hamiltonian governing the dynamics of periodically kicked systems where the kick strength is the small parameter. The expansion is formally equivalent to an infinite resummation of the Baker-Campbell-Hausdorff series in the un-driven (non-perturbed) Hamiltonian, while considering terms up to a finite order in the kick strength. As an application of the replica expansion, we analyze an Ising spin 1/2 chain periodically kicked with magnetic field of strength $h$, which has both longitudinal and transverse components. We demonstrate that even away from the regime of high frequency driving, the heating rate is nonperturbative in the kick strength bounded from above by a stretched exponential: $e^{-\mathrm{const}{h}^{-1/2}}$. This guarantees existence of a very long pre-thermal regime, where the dynamics is governed by the Floquet Hamiltonian obtained from the replica expansion.

arXiv comment5+4 pages, 1+3 figures

References in corpus (33)

• Photonic Floquet Topological Insulators
• Experimental realisation of the topological Haldane model
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Universal digital quantum simulation with trapped ions
• Equilibrium states of generic quantum systems subject to periodic driving
• Long-time behavior of periodically driven isolated interacting lattice systems
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Exponentially slow heating in periodically driven many-body systems
• Rigorous Bound on Energy Absorption and Generic Relaxation in Periodically Driven Quantum Systems
• Brillouin-Wigner theory for high-frequency expansion in periodically driven systems: Application to Floquet topological insulators
• Form factors of branch-point twist fields in quantum integrable models and entanglement entropy
• Periodically driven ergodic and many-body localized quantum systems
• Ergodic dynamics and thermalization in an isolated quantum system
• Coherent control of dressed matter waves
• Effective Hamiltonians for periodically driven systems
• Many-body energy localization transition in periodically driven systems
• Periodic thermodynamics of isolated systems
• Magnetically generated spin-orbit coupling for ultracold atoms
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit
• Dynamical Stability of a Many-body Kapitza Pendulum
• Integrable Floquet dynamics
• Dynamic stabilization of a quantum many-body spin system
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Special-case closed form of the Baker-Campbell-Hausdorff formula
• Non equilibrium phase transitions and Floquet Kibble-Zurek scaling
• A new class of completely integrable quantum spin chains
• Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems

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• Nonthermal pathways to ultrafast control in quantum materials
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems. Part II: bosons, fermions and higher spins
• Dynamical obstruction to localization in a disordered spin chain
• Quantum Time Crystals from Hamiltonians with Long-Range Interactions
• Floquet prethermalization in a Bose-Hubbard system
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• A flow equation approach to periodically driven quantum systems
• Discrete time-crystalline response stabilized by domain-wall confinement
• Almost strong 0, π edge modes in clean, interacting 1D Floquet systems
• Floquet-engineering topological transitions in a twisted transition metal dichalcogenide homobilayer
• Fermi's golden rule for heating in strongly driven Floquet systems
• Thermalization and Prethermalization in Periodically Kicked Quantum Spin Chains
• Statistical Mechanics of Floquet Quantum Matter: Exact and Emergent Conservation Laws
• Prethermalization and Thermalization in Periodically-Driven Many-Body Systems away from the High-Frequency Limit
• Renormalization Group Circuits for Weakly Interacting Continuum Field Theories
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Prethermal fragmentation in a periodically driven Fermionic chain
• Edge mode manipulation through commensurate multifrequency driving
• Pre-thermalization in a classical phonon field: slow relaxation of the number of phonons
• Flow Equations for Disordered Floquet Systems
• Emergent strong zero mode through local Floquet engineering
• Emergent symmetries in prethermal phases of periodically driven quantum systems
• Very slow heating for weakly driven quantum many-body systems
• Renyi divergences from Euclidean quenches
• Entanglement entropy and computational complexity of the Anderson impurity model out of equilibrium II: driven dynamics
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Dephasing-induced growth of discrete crystalline order in spin networks
• Integrable Floquet QFT: Elasticity and factorization under periodic driving
• On the different Floquet Hamiltonians in a periodic-driven Bose-Josephson junction
• Low-frequency and Moiré Floquet engineering: a review
• Real space thermalization of locally driven quantum magnets
• Intervalley Band Crossing and Transition of Fractional Chern Insulators in Floquet Twisted Bilayer MoTe${}_2$
• An explicit formula for perturbation theory at any order with infinitely many perturbations