Mobility edge and multifractality in a periodically driven Aubry-André model

Abstract

We study the localization-delocalization transition of Floquet eigenstates in a driven fermionic chain with an incommensurate Aubry-André potential and a hopping amplitude which is varied periodically in time. Our analysis shows the presence of a mobility edge separating single-particle delocalized states from localized and multifractal states in the Floquet spectrum. Such a mobility edge does not have any counterpart in the static Aubry-André model and exists for a range of drive frequencies near the critical frequency at which the transition occurs. The presence of the mobility edge is shown to leave a distinct imprint on fermion transport in the driven chain; it also influences the Shannon entropy and the survival probability of the fermions at long times. In addition, we find the presence of CAT states in the Floquet spectrum with weights centered around a few nearby sites of the chain. This is shown to be tied to the flattening of Floquet bands over a range of quasienergies. We support our numerical studies with a semi-analytic expression for the Floquet Hamiltonian ($H_F$) computed within a Floquet perturbation theory. The eigenspectra of the perturbative $H_F$ so obtained exhibit qualitatively identical properties to the exact eigenstates of $H_F$ obtained numerically. Our results thus constitute an analytic expression of a $H_F$ whose spectrum supports multifractal and CAT states. We suggest experiments which can test our theory.

arXiv comment17 pages, 16 figures

References in corpus (73)

• Nonequilibrium dynamics of closed interacting quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Floquet Topological Insulator in Semiconductor Quantum Wells
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Universal High-Frequency Behavior of Periodically Driven Systems: from Dynamical Stabilization to Floquet Engineering
• Topological characterization of periodically-driven quantum systems
• Atomic quantum gases in periodically driven optical lattices
• The Magnus expansion and some of its applications
• Observation of a Discrete Time Crystal
• Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
• Dynamics of a Quantum Phase Transition and Relaxation to a Steady State
• Dynamical quantum phase transitions: a review
• Equilibrium states of generic quantum systems subject to periodic driving
• Long-time behavior of periodically driven isolated interacting lattice systems
• Onset of quantum chaos in one-dimensional bosonic and fermionic systems and its relation to thermalization
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Topological singularities and the general classification of Floquet-Bloch systems
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Delocalization of a disordered bosonic system by repulsive interactions
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Floquet generation of Majorana end modes and topological invariants
• Many-body energy localization transition in periodically driven systems
• Localization and the effects of symmetries in the thermalization properties of one-dimensional quantum systems
• One-dimensional quasicrystals with power-law hopping
• Transport in the XX chain at zero temperature: Emergence of flat magnetization profiles
• Effective Theory of Floquet Topological Transitions
• Full counting statistics in a propagating quantum front and random matrix spectra
• Periodic steady state and interference in a periodically driven quantum system
• Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Quantum phase transitions in transverse field spin models: from statistical physics to quantum information
• Exact relations between multifractal exponents at the Anderson transition
• Exotic Freezing of Response in Quantum Many-Body System
• Collapse and revival of quantum many-body scars via Floquet engineering
• Scattering Theory for Floquet-Bloch States
• Logarithmic current fluctuations in non-equilibrium quantum spin chains
• Quantum dynamics with stochastic reset
• Dynamic scaling of fronts in the quantum XX chain
• Dynamics of the vacuum state in a periodically driven Rydberg chain
• Floquet dynamics in driven Fermi-Hubbard systems
• Transverse Ising Chain under Periodic Instantaneous Quenches: Dynamical Many-Body Freezing and Emergence of Solitary Oscillation
• Entanglement generation in periodically driven integrable systems: dynamical phase transitions and steady state
• Freezing a Quantum Magnet by Repeated Quantum Interference: An Experimental Realization
• Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
• Many-body Multifractality throughout Bosonic Superfluid and Mott Insulator Phases
• Many-body localization in incommensurate models with a mobility edge
• Aperiodically driven integrable systems and their emergent steady states
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Drive Induced Delocalization in Aubry-André Model
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice
• Restoring coherence via aperiodic drives in a many-body quantum system
• Dynamic freezing of strongly correlated ultracold bosons
• Prethermal quantum many-body Kapitza phases of periodically driven spin systems
• Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction
• Dynamical freezing of relaxation to equilibrium
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Non-equilibrium dynamics of quantum systems: order parameter evolution, defect generation, and qubit transfer
• Low-frequency phase diagram of irradiated graphene and periodically driven spin-1/2 $XY$ chain
• Dynamic freezing and defect suppression in the tilted one-dimensional Bose-Hubbard model
• Nonadiabatic charge pumping by oscillating potentials in one dimension: results for infinite system and finite ring
• Periodically driven integrable systems with long-range pair potentials
• Signatures and conditions for phase band crossings in periodically driven integrable systems
• Steady states of a quasiperiodically driven integrable system
• A Floquet perturbation theory for periodically driven weakly-interacting fermions
• Tuning towards dynamic freezing using a two-rate protocol
• Floquet topological transition by unpolarized light
• Disorder-induced Enhancement of Entanglement Growth in One Dimension: Information Leakage at the scale of localization length

Cited by in corpus (34)

• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Emergence of multiple localization transitions in a one-dimensional quasiperiodic lattice
• Emergent fractal phase in energy stratified random models
• Non-ergodic delocalized phase with Poisson level statistics
• Critical-to-Insulator Transitions and Fractality Edges in Perturbed Flatbands
• Anomalous multifractality in quantum chains with strongly correlated disorder
• Multiple localization transitions and novel quantum phases induced by staggered on-site potential
• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Tuning the phase diagram of a Rosenzweig-Porter model with fractal disorder
• Family-Vicsek dynamical scaling and Kardar-Parisi-Zhang-like superdiffusive growth of surface roughness in a driven one-dimensional quasiperiodic model
• Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states
• Signatures of multifractality in a periodically driven interacting Aubry-André model
• Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
• Dynamic scaling relation in quantum many-body systems
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Fully localized and partially delocalized states in the tails of Erdös-Rényi graphs in the critical regime
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Quantum multifractality as a probe of phase space in the Dicke model
• Critical dynamics of long-range quantum disordered systems
• Unconventional edge states in a two-leg ladder
• Fractal states of the Schwinger model
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Family of self-dual quasicrystals with critical Phases
• Circular Rosenzweig-Porter random matrix ensemble
• Two-strand ladder network variants: localization, multifractality, and quantum dynamics under an Aubry-André-Harper kind of quasiperiodicity
• Replica approach to the generalized Rosenzweig-Porter model
• Identifying mobility edge from finite temperature spectral form factor
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder