One dimensional quasiperiodic mosaic lattice with exact mobility edges

Abstract

The mobility edges (MEs) in energy which separate extended and localized states are a central concept in understanding the localization physics. In one-dimensional (1D) quasiperiodic systems, while MEs may exist for certain cases, the analytic results which allow for an exact understanding are rare. Here we uncover a class of exactly solvable 1D models with MEs in the spectra, where quasiperiodic on-site potentials are inlaid in the lattice with equally spaced sites. The analytical solutions provide the exact results not only for the MEs, but also for the localization and extended features of all states in the spectra, as derived through computing the Lyapunov exponents from Avila's global theory, and also numerically verified by calculating the fractal dimension. We further propose a novel scheme with experimental feasibility to realize our model based on an optical Raman lattice, which paves the way for experimental exploration of the predicted exact ME physics.

arXiv commentTo appear in PRL

References in corpus (38)

• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Coupling Identical 1D Many-Body Localized Systems
• 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
• Most efficient quantum thermoelectric at finite power output
• Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Observation of many-body localization in a one-dimensional system with single-particle mobility edge
• One-dimensional quasicrystals with power-law hopping
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Absence of many-body mobility edges
• Observation of symmetry-protected topological band with ultracold fermions
• Observation of a disordered bosonic insulator from weak to strong interactions
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Engineering a flux-dependent mobility edge in disordered zigzag chains
• High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases
• Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
• Many-body critical phase: extended and nonthermal
• Realization and detection of non-ergodic critical phases in optical Raman lattice
• Dirac, Rashba and Weyl type spin-orbit couplings: toward experimental realization in ultracold atoms
• Anderson Localization of cold atomic gases with effective spin-orbit interaction in a quasiperiodic optical lattice
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Anomalous transport through algebraically localized states in one-dimension
• Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices
• Thermoelectricity near Anderson localization transitions
• Quasiperiodic quantum heat engines with a mobility edge
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Localization problem of the quasiperiodic system with the spin orbit interaction
• Spectral statistics, finite-size scaling and multifractal analysis of quasiperiodic chain with p-wave pairing
• Investigating many-body mobility edges in isolated quantum systems
• Localization driven superradiant instability

Cited by in corpus (137)

• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Exact new mobility edges between critical and localized states
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Polariton Localization and Dispersion Properties of Disordered Quantum Emitters in Multimode Microcavities
• Emergence of multiple localization transitions in a one-dimensional quasiperiodic lattice
• Hidden dualities in 1D quasiperiodic lattice models
• Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains
• Quantum phase with coexisting localized, extended, and critical zones
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential
• Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
• Dephasing-induced mobility edges in quasicrystals
• Critical analysis of the re-entrant localization transition in a one-dimensional dimerized quasiperiodic lattice
• Quantum criticality and universality in the $p$-wave paired Aubry-André-Harper model
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Self-consistent theory of mobility edges in quasiperiodic chains
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Coexistence of localization and transport in many-body two-dimensional Aubry-André models
• Dissipation induced extended-localized transition
• The general approach to the critical phase with coupled quasiperiodic chains
• Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
• Single-Particle Mobility Edge without Disorder
• Multiple localization transitions and novel quantum phases induced by staggered on-site potential
• Exact mobility edges for 1D quasiperiodic models
• Absence of Mobility Edge in Short-range Uncorrelated Disordered Model: Coexistence of Localized and Extended States
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Quantum Mpemba effect of localization in the dissipative mosaic model
• Critical and Topological Phases of Dimerized Kitaev Chain in Presence of Quasiperiodic Potential
• Probing multi-mobility edges in quasiperiodic mosaic lattices
• Critical states and anomalous mobility edges in two-dimensional diagonal quasicrystals
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• 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
• Topological phases and Anderson localization in off-diagonal mosaic lattices
• Universal subdiffusive behavior at band edges from transfer matrix exceptional points
• Non-Hermitian topology and criticality in photonic arrays with engineered losses
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic 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
• 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
• Electrical analogue of one-dimensional and quasi-one-dimensional Aubry-André-Harper lattices
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• The fundamental localization phases in quasiperiodic systems: A unified framework and exact results
• Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
• Hidden self-duality and exact mobility edges in quasiperiodic network models
• Coexistence of ergodic and weakly ergodic states in finite-height Wannier-Stark ladders
• Fate of localization in coupled free chain and disordered chain
• Mobility edges and critical regions in periodically kicked incommensurate optical Raman lattice
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Mobility Edges in one-dimensional Models with quasi-periodic disorder
• Non-Hermitian control of localization in mosaic photonic lattices
• Equivalence and superposition of real and imaginary quasiperiodicities
• Fate of non-Hermitian free fermions with Wannier-Stark ladder
• Multiple intermediate phases in the interpolating Aubry-André-Fibonacci model
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Localisation in quasiperiodic chains: a theory based on convergence of local propagators
• Dynamical localization in non-Hermitian quasi-crystals
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Transport and localization properties of excitations in one-dimensional lattices with diagonal disordered mosaic modulations
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Resonances, mobility edges and gap-protected Anderson localization in generalized disordered mosaic lattices
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Quantum criticality of generalized Aubry-André models with exact mobility edges using fidelity susceptibility
• Exact mobility edges for almost-periodic CMV matrices via gauge symmetries
• Exploring Multifractal Critical Phases in Two-Dimensional Quasiperiodic Systems
• Anderson Localization and Swing Mobility Edge in Curved Spacetime
• 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
• Imbalance for a family of one-dimensional incommensurate models with mobility edges
• Wave functions in the Critical Phase: a Planar \textit{Sierpiński} Fractal Lattice
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Quantum Transports in Two-Dimensions with Long Range Hopping: Shielding, Localization and the Extended Isolated State
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Robust extended states in Anderson model on partially disordered random regular graphs
• Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• The odd-even effect of mosaic modulation period of quasi-periodic hopping on the Anderson localization in a one-dimensional lattice model
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Bound states in one-dimensional systems with colored noise
• Exact mobility edges in quasiperiodic network models with slowly varying potentials
• Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks
• Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
• Subsystem localization in a two-leg ladder system
• Entanglement growth and information capacity in a quasiperiodic system with a single-particle mobility edge
• Interacting quasiperiodic spin chains in the prethermal regime
• Convection-modulated topological edge mode and extended-localized criticality in thermal metamaterials
• Arithmetic Phase Transitions For Mosaic Maryland Model
• Topological Anderson insulator phases in one dimensional quasi-periodic mechanical SSH chains
• Entanglement entropy scaling in critical phases of 1D quasiperiodic systems
• Level spacing distribution of localized phases induced by quasiperiodic potentials
• Phase Properties of Interacting Bosons in Presence of Quasiperiodic and Random Disorder
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Types of dynamical behavior in a quasiperiodic mosaic lattice
• Multifractality in high-dimensional graphs induced by correlated radial disorder
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• A General Strategy for Realizing Mpemba Effects in Open Quantum Systems
• Experimental observation of exact quantum critical states
• Anomalous universal quantum transport in 2D asymptotic quasiperiodic system
• Transport through Quantum Anomalous Hall Bilayers with Lattice Mismatch
• Family of self-dual quasicrystals with critical Phases
• Localization and Topology in Noncentrosymmetric Superconductors with Disorder
• From percolation transition to Anderson localization in one-dimensional speckle potentials
• Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge
• Delocalization in a partially disordered interacting many-body system
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Fractal Quasicondensation in One Dimension
• Supercorrelated decay in a quasiperiodic nonlinear waveguide: From Markovian to non-Markovian transitions
• Exact mobility edges in a slowly varying quasiperiodic ladder model
• Entanglement entropy as a probe of topological phase transitions
• Quantum localization in incommensurate tight-binding chains
• Exact Mobility Edges in a Disorder-Free Dimerized Stark Lattice with Effective Unbounded Hopping
• Topological Anderson insulator and reentrant topological transitions in a mosaic trimer lattice
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Localization phase diagram of the Hexagonal Lattice with irrational magnetic flux
• Fluctuation-stable generalized entropy probes of spectral heterogeneity
• 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
• Arithmetic Tuning of Dynamical Critical Exponents in Quasiperiodic Localization Transitions
• Topological edge states and disorder robustness in one-dimensional off-diagonal mosaic lattices