A flow equation approach to periodically driven quantum systems

Abstract

We present a theoretical method to generate a highly accurate {\em time-independent} Hamiltonian governing the finite-time behavior of a time-periodic system. The method exploits infinitesimal unitary transformation steps, from which renormalization group-like flow equations are derived to produce the effective Hamiltonian. Our tractable method has a range of validity reaching into frequency regimes that are usually inaccessible via high frequency $\omega$ expansions in the parameter $h/\omega$, where $h$ is the upper limit for the strength of local interactions. We demonstrate our approach on both interacting and non-interacting many-body Hamiltonians where it offers an improvement over the more well-known Magnus expansion and other high frequency expansions. For the interacting models, we compare our approximate results to those found via exact diagonalization. While the approximation generally performs better globally than other high frequency approximations, the improvement is especially pronounced in the regime of lower frequencies and strong external driving. This regime is of special interest because of its proximity to the resonant regime where the effect of a periodic drive is the most dramatic. Our results open a new route towards identifying novel non-equilibrium regimes and behaviors in driven quantum many-particle systems.

25 pages, 14 figures

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• Dynamical Freezing and Scar Points in Strongly Driven Floquet Matter: Resonance vs Emergent Conservation Laws
• Analytic approaches to periodically driven closed quantum systems: Methods and Applications
• Effective Floquet Hamiltonians for periodically-driven twisted bilayer graphene
• Floquet engineering of interlayer couplings: Tuning the magic angle of twisted bilayer graphene at the exit of a waveguide
• 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
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Phonon-mediated dimensional crossover in bilayer CrI3
• Exact dynamics of quantum systems driven by time-varying Hamiltonians: solution for the Bloch-Siegert Hamiltonian and applications to NMR
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Dynamical properties of a driven dissipative dimerized $S=1/2$ chain
• Floquet spectrum for anisotropic and tilted Dirac materials under linearly polarized light at all field intensities
• Floquet Prethermal Phase Protected by U(1) Symmetry on a Superconducting Quantum Processor
• Generating Synthetic Magnetism via Floquet Engineering Auxiliary Qubits in Phonon-Cavity-Based Lattice
• Analogue of Hamilton-Jacobi theory for the time-evolution operator
• Flow Equations for Disordered Floquet Systems
• Efficient flow equations for dissipative systems
• Divergence of the Floquet-Magnus expansion in a periodically driven one-body system with energy localization
• Fano resonances in optical spectra of semiconductor quantum wells driven by an oscillating field
• Local integrals of motion and the stability of many-body localisation in Wannier-Stark potentials
• Tuning of Bilayer Graphene Heterostructure by Horizontally Incident Circular Polarized Light
• Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy
• Photoinduced prethermal order parameter dynamics in the two-dimensional large-$N$ Hubbard-Heisenberg model
• Spin dynamics under the influence of elliptically rotating fields: Extracting the field topology from time-averaged quantities
• Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
• Disorder-induced spin-charge separation in the 1-D Hubbard model
• The Future of the Correlated Electron Problem
• Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light
• Quench dynamics in the one-dimensional mass-imbalanced ionic Hubbard model
• Floquet engineering and non-equilibrium topological maps in twisted trilayer graphene