Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice

Abstract

We propose a geometric series modulated non-Hermitian quasiperiodic lattice model, and explore its localization and topological properties. The results show that with the ever-increasing summation terms of the geometric series, multiple mobility edges and non-Hermitian point gaps with high winding number can be induced in the system. The point gap spectrum of the system has a multi-loop nested structure in the complex plane, resulting in a high winding number. In addition, we analyze the limit case of summation of infinite terms. The results show that the mobility edges merge together as only one mobility edge when summation terms are pushed to the limit. Meanwhile, the corresponding point gaps are merged into a ring with winding number equal to one. Through Avila's global theory, we give an analytical expression for mobility edges in the limit of infinite summation, reconfirming that mobility edges and point gaps do merge and will result in a winding number that is indeed equal to one.

12 pages, 11 figures

References in corpus (76)

• Anderson Transitions
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Topological States and Adiabatic Pumping in Quasicrystals
• Correspondence between winding numbers and skin modes in non-hermitian systems
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Topological Anderson Insulator
• Spectral signatures of many-body localization with interacting photons
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Topological phase transition in non-Hermitian quasicrystals
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Interplay of non-Hermitian skin effects and Anderson localization in non-reciprocal quasiperiodic lattices
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Topological quantum matter with cold atoms
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Anderson localization in Bose-Einstein condensates
• One-dimensional quasicrystals with power-law hopping
• Fractal energy spectrum of a polariton gas in a Fibonacci quasi-periodic potential
• 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
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Localization and adiabatic pumping in a generalized Aubry-André-Harper model
• Reentrant Localization Transition in a Quasiperiodic Chain
• Skin effect and winding number in disordered non-Hermitian systems
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian Topological Anderson Insulators
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Engineering a flux-dependent mobility edge in disordered zigzag chains
• Many-body localization in a non-Hermitian quasi-periodic system
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
• Exact new mobility edges between critical and localized states
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Unitary and non-unitary quantum cellular automata with Rydberg arrays
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Quantum coarsening and collective dynamics on a programmable simulator
• Emergence of multiple localization transitions in a one-dimensional quasiperiodic lattice
• Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• 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
• Non-Hermitian Maryland Model
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Entanglement phase transitions in non-Hermitian quasicrystals
• The general approach to the critical phase with coupled quasiperiodic chains
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Double exceptional links in a three-dimensional dissipative cold atomic gas
• Exact mobility edges for 1D quasiperiodic models
• Scaling and renormalization in the modern theory of polarization: application to disordered systems
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
• Damping transition in an open generalized Aubry-André-Harper model
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model
• Signatures of multifractality in a periodically driven interacting Aubry-André model
• Localization via Quasi-Periodic Bulk-Bulk Correspondence
• Entanglement phase transitions in non-Hermitian Floquet systems
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Anderson Localization and Swing Mobility Edge in Curved Spacetime

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