Quasiperiodicity hinders ergodic Floquet eigenstates

Abstract

Quasiperiodic systems in one dimension can host non-ergodic states, e.g. localized in position or momentum. Periodic quenches within localized phases yield Floquet eigenstates of the same nature, i.e. spatially localized or ballistic. However, periodic quenches across these two non-ergodic phases were thought to produce ergodic diffusive-like states even for non-interacting particles. We show that this expectation is not met at the thermodynamic limit where the system always attains a non-ergodic state. We find that ergodicity may be recovered by scaling the Floquet quenching period with system size and determine the corresponding scaling function. Our results suggest that while the fraction of spatially localized or ballistic states depends on the model's details, all Floquet eigenstates belong to one of these non-ergodic categories. Our findings demonstrate that quasiperiodicity hinders ergodicity and thermalization, even in driven systems where these phenomena are commonly expected.

References in corpus (74)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Experimental realisation of the topological Haldane model
• Anderson Transitions
• Localization of interacting fermions at high temperature
• Anderson localization of a non-interacting Bose-Einstein condensate
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• On the phase structure of driven quantum systems
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates
• Majorana Fermions in Equilibrium and Driven Cold Atom Quantum Wires
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Long-time behavior of periodically driven isolated interacting lattice systems
• Many-body localization in periodically driven systems
• Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
• Fate of many-body localization under periodic driving
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Quantum chaos challenges many-body localization
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Periodically driven ergodic and many-body localized quantum systems
• Periodically Driving a Many-Body Localized Quantum System
• Two universality classes for the many-body localization transition
• Classification of Interacting Topological Floquet Phases in One Dimension
• A random matrix model with localization and ergodic transitions
• Distinguishing localization from chaos: challenges in finite-size systems
• A theory of many-body localization in periodically driven systems
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Mutifractal Analysis of Broadly Distributed Observables at Criticality
• Flat Bands Under Correlated Perturbations
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Challenges to observation of many-body localization
• Non-ergodic phases in strongly disordered random regular graphs
• Correlation-induced localization
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Anomalous mobility edges in one-dimensional quasiperiodic models
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Stroboscopic prethermalization in weakly interacting periodically driven systems
• Flatband Engineering of Mobility Edges
• Anderson localization transitions with and without random potentials
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Transport properties across the many-body localization transition in quasiperiodic and random systems
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Robustness of delocalization to the inclusion of soft constraints in long-range random models
• Drive Induced Delocalization in Aubry-André Model
• Floquet Thermalization: Symmetries and Random Matrix Ensembles
• Mobility edge and multifractality in a periodically driven Aubry-André model
• Hidden dualities in 1D quasiperiodic lattice models
• Stability of many-body localization in Floquet systems
• Localization, topology and quantized transport in disordered Floquet systems
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Non-ergodic delocalized phase with Poisson level statistics
• Long-lived period-doubled edge modes of interacting and disorder-free Floquet spin chains
• Thermalization in a periodically driven fully-connected quantum Ising ferromagnet
• How periodic driving heats a disordered quantum spin chain
• Signature of Chaos and Delocalization in a Periodically Driven Many Body System : An Out-of-Time-Order Correlation Study
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Localization and transport in a strongly driven Anderson insulator
• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Edge and bulk localization of Floquet topological superconductors
• Regimes of heating and dynamical response in driven many-body localized systems
• Floquet topological $d+id$ superconductivity induced by chiral many-body interactions
• Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling
• Quasiperiodic driving of Anderson localized waves in one dimension
• Dimer Decimation and Intricately Nested Localized-Ballistic Phases of Kicked Harper
• Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
• Localisation Transition in the Driven Aubry-André Model

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• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
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• Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
• Robust extended states in Anderson model on partially disordered random regular graphs
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder