Anomalous transport through algebraically localized states in one-dimension

Abstract

Localization in one-dimensional disordered or quasiperiodic non-interacting systems in presence of power-law hopping is very different from localization in short-ranged systems. Power-law hopping leads to algebraic localization as opposed to exponential localization in short-ranged systems. Exponential localization is synonymous with insulating behavior in the thermodynamic limit. Here we show that the same is not true for algebraic localization. We show, on general grounds, that depending on the strength of the algebraic decay, the algebraically localized states can be actually either conducting or insulating in thermodynamic limit. We exemplify this statement with explicit calculations on the Aubry-André-Harper model in presence of power-law hopping, with the power-law exponent $\alpha >1$, so that the thermodynamic limit is well-defined. We find a phase of this system where there is a mobility edge separating completely delocalized and algebraically localized states, with the algebraically localized states showing signatures of super-diffusive transport. Thus, in this phase, the mobility edge separates two kinds of conducting states, ballistic and super-diffusive. We trace the occurrence of this behavior to near-resonance conditions of the on-site energies that occur due to the quasi-periodic nature of the potential.

References in corpus (67)

• Topological States and Adiabatic Pumping in Quasicrystals
• Observation of a Discrete Time Crystal
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Exploring the many-body localization transition in two dimensions
• Fundamental aspects of steady-state conversion of heat to work at the nanoscale
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• Observation of the Meissner effect with ultracold atoms in bosonic ladders
• Electron Localization in the Insulating State
• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Polarization and localization in insulators: generating function approach
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Signatures of Many-Body Localization in a Controlled Open Quantum System
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• Entanglement entropy for the long range Ising chain
• Many-body Localization with Dipoles
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• Kitaev chains with long-range pairing
• Floquet time crystal in the Lipkin-Meshkov-Glick model
• One-dimensional quasicrystals with power-law hopping
• Entanglement growth in quench dynamics with variable range interactions
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Dynamical phase diagram of spin chains with long-range interactions
• Environment-assisted quantum transport in a 10-qubit network
• Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
• Correlation-induced localization
• Many body localization in the presence of a single particle mobility edge
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Observation of a Transition Between Dynamical Phases in a Quantum Degenerate Fermi Gas
• Interaction instability of localization in quasiperiodic systems
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Localization in a random $x-y$ model with the long-range interaction: Intermediate case between single particle and many-body problems
• Metal-insulator transition in an aperiodic ladder network: an exact result
• Localization transitions and mobility edges in coupled Aubry-André chains
• Machine Learning Many-Body Localization: Search for the Elusive Nonergodic Metal
• Quasi-localized excitations induced by long-range interactions in translationally-invariant quantum spin chains
• Duality in power-law localization in disordered one-dimensional systems
• Entanglement area laws for long-range interacting systems
• Self-dual quasiperiodic systems with power-law hopping
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Anomalous transport in the Aubry-André-Harper model in isolated and open systems
• Shielding and localization in presence of long range hopping
• Entanglement and fluctuations in the XXZ model with power-law interactions
• Chaotic dynamical ferromagnetic phase induced by non-equilibrium quantum fluctuations
• Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Algebraic Many-Body Localization and its implications on information propagation
• Drude weight in systems with open boundary conditions
• Effect of long-range hopping and interactions on entanglement dynamics and many-body localization
• Monitoring the localization-delocalization transition within a 1D model with non-random long-range interaction
• Heat current rectification and mobility edges
• Polarization fluctuations in insulators and metals: New and old theories merge
• Prethermalization and dynamical transition in an isolated trapped ion spin chain
• Prethermalization in the transverse-field Ising chain with long-range interactions
• Entanglement contour perspective for strong area law violation in a disordered long-range hopping model
• Criterion for the occurrence of many body localization in the presence of a single particle mobility edge
• Classifying transport behavior via current fluctuations in open quantum systems
• Phase coherence in tight-binding models with nonrandom long-range hopping
• Particle current rectification in a quasi-periodic double-stranded ladder
• Genuine localisation transition in a long-range hopping model
• High degree of current rectification at nanoscale level
• Multifractality in the generalized Aubry-Andre quasiperiodic localization model with power-law hoppings or power-law Fourier coefficients
• More current with less particles due to power-law hopping

Cited by in corpus (33)

• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Quantum phase with coexisting localized, extended, and critical zones
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Dissipation induced extended-localized transition
• Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
• Single-Particle Mobility Edge without Disorder
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Many-body localization in long range model: Real space renormalization group study
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
• Sub-diffusive phases in open clean long-range systems
• Dynamics of fluctuation correlation in periodically driven classical system
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice
• Mobility Edges in one-dimensional Models with quasi-periodic disorder
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations
• Superdiffusive transport on lattices with nodal impurities
• Read-out of Quasi-periodic Systems using Qubits
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• One-dimensional L{é}vy Quasicrystal
• Unraveling Multifractality and Mobility Edges in Quasiperiodic Aubry-André-Harper Chains through High-Harmonic Generation
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Inducing a transition between thermal and many-body localized states and detecting many-body mobility edges through dissipation
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Structural constraints on mobility edges in one-dimensional quasiperiodic systems
• Superdiffusive transport in chaotic quantum systems with nodal interactions
• Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
• Quantum transport in quasi-periodic lattice systems in presence of Büttiker probes