Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials

Abstract

Quasiperiodic systems offer an appealing intermediate between long-range ordered and genuine disordered systems, with unusual critical properties. One-dimensional models that break the so-called self-dual symmetry usually display a mobility edge, similarly as truly disordered systems in dimension strictly higher than two. Here, we determine the critical localization properties of single particles in shallow, one-dimensional, quasiperiodic models and relate them to the fractal character of the energy spectrum. On the one hand, we determine the mobility edge and show that it separates the localized and extended phases, with no intermediate phase. On the other hand, we determine the critical potential amplitude and find the universal critical exponent $\nu \simeq 1/3$. We also study the spectral Hausdorff dimension and show that it is nonuniversal but always smaller than unity, hence showing that the spectrum is nowhere dense. Finally, applications to ongoing studies of Anderson localization, Bose-glass physics, and many-body localization in ultracold atoms are discussed.

References in corpus (34)

• Random-Matrix Theory of Quantum Transport
• Anderson Transitions
• Probing entanglement in a many-body-localized system
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Many-Body Localization in a Quasiperiodic System
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Fermi-Bose quantum degenerate ^40 K - ^87 Rb mixture with attractive interaction
• Disordered quantum gases under control
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Atomic Bose and Anderson glasses in optical lattices
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Anderson localization in Bose-Einstein condensates
• Quantum critical behavior at the many-body-localization transition
• Phase Diagram of Bosonic Atoms in Two-Color Superlattices
• The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Matter-wave diffraction from a quasicrystalline optical lattice
• Ultracold Bose Gases in 1D Disorder: From Lifshits Glass to Bose-Einstein Condensate
• Observation of a disordered bosonic insulator from weak to strong interactions
• Glassy behavior in a binary atomic mixture
• Bose-Einstein Condensates in Optical Quasicrystal Lattices
• Bosons in one-dimensional incommensurate superlattices
• Transport of a Bose gas in 1D disordered lattices at the fluid-insulator transition
• Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices
• Non-power-law universality in one-dimensional quasicrystals
• Measurement of spectral functions of ultracold atoms in disordered potentials
• Localized and extended states in a disordered trap
• Elastic Scattering Time of Matter-Waves in Disordered Potentials
• Quantum simulation of a 2D quasicrystal with cold atoms
• Finite-temperature effects on interacting bosonic 1D systems in disordered lattices

Cited by in corpus (121)

• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Many-body localization in a non-Hermitian quasi-periodic system
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
• Exact new mobility edges between critical and localized states
• Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
• Quantum time reflection and refraction of ultracold atoms
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Hidden dualities in 1D quasiperiodic lattice models
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Universality and Quantum Criticality in Quasiperiodic Spin Chains
• Quantum phase with coexisting localized, extended, and critical zones
• Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Topological properties of the long-range Kitaev chain with Aubry-André-Harper modulation
• Dephasing-induced mobility edges in quasicrystals
• Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice
• Self-consistent theory of mobility edges in quasiperiodic chains
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Topologically quantized current in quasiperiodic Thouless pumps
• The general approach to the critical phase with coupled quasiperiodic chains
• Dissipation induced extended-localized transition
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Local Integrals of Motion in Quasiperiodic Many-Body Localized Systems
• Quantum Mpemba effect of localization in the dissipative mosaic model
• Many-body localization in Bose-Hubbard model: evidence for the mobility edge
• Thermodynamic Phase Diagram of Two-Dimensional Bosons in a Quasicrystal Potential
• Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
• Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Quantum criticality in the disordered Aubry-André model
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Enhanced Amplitude for Superconductivity due to Spectrum-wide Wave Function Criticality in Quasiperiodic and Power-law Random Hopping Models
• Emergence of quasiperiodic Bloch wave functions in quasicrystals
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Exploring unconventional quantum criticality in the p-wave-paired Aubry-André-Harper model
• Quasiperiodic disorder induced critical phases in a periodically driven dimerized $p$-wave Kitaev chain
• Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Mott transition for a Lieb-Liniger gas in a shallow quasiperiodic potential: Delocalization induced by disorder
• Quench Spectroscopy of a Disordered Quantum System
• Mobility Edges in one-dimensional Models with quasi-periodic disorder
• Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Dimers and discrete breathers in Bose-Einstein condensates in a quasi-periodic potential
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators
• Bloch-Landau-Zener oscillations in a quasi-periodic potential
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Localization and topological transitions in generalized non-Hermitian SSH models
• Anderson Localization and Swing Mobility Edge in Curved Spacetime
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Strongly interacting bosons in 1D disordered lattice: phase coherence of distorted Mott phases
• Dissipation induced transition between delocalization and localization in the three-dimensional Anderson model
• Read-out of Quasi-periodic Systems using Qubits
• Non-Abelian gauge potential driven localization transition in quasiperiodic optical lattices
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-André-Harper Chains through High-Harmonic Generation
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Stability of dipolar bosons in a quasiperiodic potential
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Measurement-induced phase transitions for free fermions in a quasiperiodic potential
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Experimental observation of exact quantum critical states
• Phase Properties of Interacting Bosons in Presence of Quasiperiodic and Random Disorder
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Effects of forward disorder on quasi-1D superconductors
• Quasiperiodic Quadrupole Insulators
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
• Fate of Quadratic Band Crossing under quasiperiodic modulation
• Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation
• Energy Spectrum Theory of Incommensurate Systems
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions
• Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model
• Reentrant localization in a quasiperiodic chain with correlated hopping sequences
• Localization Transition for Interacting Quantum Particles in Colored-Noise Disorder
• Multistable localized states in highly photonic polariton rings with a quasiperiodic modulation
• Formation of nonlinear modes in one-dimensional quasiperiodic lattices with a mobility edge
• Exact mobility edges in a slowly varying quasiperiodic ladder model
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Towards the complete description of stationary states of a Bose-Einstein condensate in a one-dimensional quasiperiodic lattice: A coding approach
• Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential
• Fluctuation-stable generalized entropy probes of spectral heterogeneity
• Correlated disorder induced anomalous transport in magnetically doped topological insulators
• Metal-Insulator Coexistence and Gap-Crossing Domain-Wall Modes in an Aubry-André Model with Nonlocal Hopping
• Distinct reentrant transitions in a quasi-periodic Raman lattice
• Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Fractal Quasicondensation in One Dimension
• Dynamical localization of interacting ultracold atoms in one-dimensional quasi-periodic potentials
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping