Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
arXiv:0907.0252 · doi:10.1103/PhysRevA.80.021603
Abstract
Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-André (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schrödinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.
5 pages, 6 figures
References in corpus (3)
Cited by in corpus (121)
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
- Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
- Mobility Edges in 1D Bichromatic Incommensurate Potentials
- One dimensional quasiperiodic mosaic lattice with exact mobility edges
- Anderson localization in Bose-Einstein condensates
- Observation of tunable mobility edges in generalized Aubry-André lattices
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Topological Phases in Non-Hermitian Aubry-André-Harper Models
- Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
- Localization and adiabatic pumping in a generalized Aubry-André-Harper model
- Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
- Observation of interaction-induced mobility edge in a disordered atomic wire
- Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasi-periodic potentials
- Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
- Exact new mobility edges between critical and localized states
- Universal properties of many-body localization transitions in quasiperiodic systems
- Strongly-Interacting Bosons in a Two-Dimensional Quasicrystal Lattice
- Many-body delocalization dynamics in long Aubry-André quasiperiodic chains
- Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
- Localization of a spin-orbit coupled Bose-Einstein condensate in a bichromatic optical lattice
- The Aubry-André model as the hobbyhorse for understanding localization phenomenon
- Many-body localization in incommensurate models with a mobility edge
- Multifractality without fine-tuning in a Floquet quasiperiodic chain
- Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
- Mobility edge and multifractality in a periodically driven Aubry-André model
- Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
- Quantum phase with coexisting localized, extended, and critical zones
- Quasiperiodic quantum heat engines with a mobility edge
- Nonlinear lattice waves in heterogeneous media
- Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
- Dynamical evolution in a one-dimensional incommensurate lattice with symmetry
- Duality between two generalized Aubry-Andre models with exact mobility edges
- Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
- Localization of a Bose-Einstein condensate vortex in a bichromatic optical lattice
- Dephasing-induced mobility edges in quasicrystals
- Probing many-body localization by excited-state VQE
- Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice
- Quantum phases and topological properties of interacting fermions in one-dimensional superlattices
- Self-consistent theory of mobility edges in quasiperiodic chains
- The quasi-periodic quantum Ising transition in 1D
- Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
- Superfluid to Bose-glass transition of hard core bosons in one-dimensional incommensurate optical lattice
- Environment-assisted quantum transport and mobility edges
- Dissipation induced extended-localized transition
- The general approach to the critical phase with coupled quasiperiodic chains
- Single-Particle Mobility Edge without Disorder
- Wave interactions in localizing media - a coin with many faces
- Symmetry breaking in a localized interacting binary BEC in a bi-chromatic optical lattice
- Criterion for the occurrence of many body localization in the presence of a single particle mobility edge
- Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
- Hubbard Models for Quasicrystalline Potentials
- Fate of topological states in incommensurate generalized Aubry-André models
- Spatially-antisymmetric localization of matter wave in a bichromatic optical lattice
- Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
- Probing multi-mobility edges in quasiperiodic mosaic lattices
- Localization driven superradiant instability
- Engineering mobility in quasiperiodic lattices with exact mobility edges
- Dynamical Scaling of Surface Roughness and Entanglement Entropy in Disordered Fermion Models
- Quantum criticality in Ising chains with random hyperuniform couplings
- Topological phases and Anderson localization in off-diagonal mosaic lattices
- Strongly interacting bosons in multi-chromatic potentials supporting mobility edges: localization, quasi-condensation and expansion dynamics
- Critical integer quantum Hall topology and the integrable Maryland model as a topological quantum critical point
- Quantum criticality in the disordered Aubry-André model
- Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
- A proposed signature of Anderson localization and correlation-induced delocalization in an N-leg optical lattice
- Localization of ultracold atoms in incommensurate spin-orbit-coupling and Zeeman lattices
- Signatures of multifractality in a periodically driven interacting Aubry-André model
- Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
- Observation of reentrant metal-insulator transition in a random-dimer disordered SSH lattice
- Counterdiabatic control of transport in a synthetic tight-binding lattice
- Periodically and Quasi-periodically Driven Dynamics of Bose-Einstein Condensates
- Localization on a synthetic Hall cylinder
- Phase diagram of a generalized off-diagonal Aubry-André model with p-wave pairing
- Quantum transport in a one-dimensional quasicrystal with mobility edges
- Quantum Dynamics of Disordered Bosons in an Optical Lattice
- Kibble-Zurek scaling in one-dimensional localization transitions
- Fate of localization in coupled free chain and disordered chain
- Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice
- Mobility Edges in one-dimensional Models with quasi-periodic disorder
- Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
- Localization of interacting Fermi gases in quasiperiodic potentials
- Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
- Effect of loss on the topological features of dimer chain described by the extended Aubry-André-Harper model
- Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices
- Electronic States in One, Two, and Three Dimensional Highly Amorphous Materials: A Tight Binding Treatment
- One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential
- Bloch-Landau-Zener oscillations in a quasi-periodic potential
- Localisation in quasiperiodic chains: a theory based on convergence of local propagators
- Phase transition in a Aubry-Andre system with rapidly oscillating magnetic field
- Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
- Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
- Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
- Dissipation induced transition between delocalization and localization in the three-dimensional Anderson model
- Lattice bosons in a quasi-disordered environment: The effects of next-nearest-neighbor hopping on localization and Bose-Einstein condensation
- Out-of-equilibrium dynamics of repulsive Fermi gases in quasi-periodic potentials: a Density Functional Theory study
- Unveiling quantum criticality of disordered Aubry-André-Harper models via typical fidelity susceptibility
- Imbalance for a family of one-dimensional incommensurate models with mobility edges
- Inducing a transition between thermal and many-body localized states and detecting many-body mobility edges through dissipation
- Generalized Aubry-Andre-Harper Models in Optical Superlattices
- Localization and persistent currents in a quasiperiodic disordered helical lattice
- Localized Floquet modes in arrays of out-of-phase curved waveguides with a quasiperiodic modulation
- Multifractality in high-dimensional graphs induced by correlated radial disorder
- Level spacing distribution of localized phases induced by quasiperiodic potentials
- Phase Properties of Interacting Bosons in Presence of Quasiperiodic and Random Disorder
- Structural constraints on mobility edges in one-dimensional quasiperiodic systems
- Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions
- Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems
- Quantum Adiabatic Doping for Atomic Fermi-Hubbard Quantum Simulations
- Formation of nonlinear modes in one-dimensional quasiperiodic lattices with a mobility edge
- Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
- Multistable localized states in highly photonic polariton rings with a quasiperiodic modulation
- Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation
- Phase Transitions and Critical Behavior in Quasi-One-Dimensional Two-Channel Systems with Quasiperiodic Disorder
- Quantum localization in incommensurate tight-binding chains
- Bloch-Landau-Zener Oscillations in Moiré Lattices
- 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
- Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
- Many-body localization in a slowly varying potential
- Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals