Universality classes of thermalization for mesoscopic Floquet systems

Abstract

We identify several phases of thermalization that describe regimes of behavior in isolated, periodically driven (Floquet), mesoscopic quantum chaotic systems. We also identify a new Floquet thermal ensemble -- the ladder ensemble -- that is qualitatively distinct from the featureless infinite-temperature state that is often assumed to describe the equilibrium of driven systems. The phases can be coarsely classified by (i) whether or not the system irreversibly exchanges energy of order $\omega$ with the drive, i.e., Floquet thermalizes, and (ii) the ensemble describing the final equilibrium in systems that do Floquet thermalize. These phases represent regimes of behavior in mesoscopic systems, but they are sharply defined in a large-system limit where the drive frequency $\omega$ scales up with system size $N$ as the $N\to \infty$ limit is taken: we examine frequency scalings ranging from a weak $\omega \sim \log N$, to stronger scalings ranging from $\omega \sim \sqrt{N}$ to $\omega \sim N$. We show that the transition where Floquet thermalization breaks down occurs at $\omega \sim N$ and, beyond that, systems that do not Floquet thermalize are distinguished based on the presence or absence of rare resonances across Floquet zones. We produce a thermalization phase diagram that is relevant for numerical studies of Floquet systems and experimental studies on small-scale quantum simulators, both of which lack a separation of scales between $N$ and $\omega$. A striking prediction of our work is that, under perfect isolation, certain realistic quench protocols from simple pure initial states can show Floquet thermalization to a novel type of Schrodinger-cat state that is a global superposition of states at distinct temperatures. Our work extends and organizes the theory of Floquet thermalization, heating, and equilibrium into the setting of mesoscopic quantum systems.

18 pages, 8 figures

References in corpus (29)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Equilibrium states of generic quantum systems subject to periodic driving
• Many-body localization in periodically driven systems
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• Breakdown of thermalization in finite one-dimensional systems
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Avalanches and many-body resonances in many-body localized systems
• Quantum Many-Body Scars: A Quasiparticle Perspective
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Dynamical obstruction to localization in a disordered spin chain
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Eta-Pairing in Hubbard Models: From Spectrum Generating Algebras to Quantum Many-Body Scars
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• A constructive theory of the numerically accessible many-body localized to thermal crossover
• Instability of many-body localized systems as a phase transition in a nonstandard thermodynamic limit
• Thermalization of dilute impurities in one dimensional spin chains
• Phenomenology of the Prethermal Many-Body Localized Regime
• A statistical mechanism for operator growth
• Onset of many-body quantum chaos due to breaking integrability
• Local resonances and parametric level dynamics in the many-body localised phase
• Discrete time-crystalline response stabilized by domain-wall confinement
• Fermi's golden rule for heating in strongly driven Floquet systems
• Resonant energy scales and local observables in the many-body localised phase
• Simulation of quantum many-body dynamics with Tensor Processing Units: Floquet prethermalization
• Emergence of Fermi's Golden Rule
• Heating Rates under Fast Periodic Driving beyond Linear Response
• Estimating heating times in periodically driven quantum many-body systems via avoided crossing spectroscopy

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