Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice

Abstract

We analytically determine the non-Hermitian mobility edges of a one-dimensional quasiperiodic lattice model with exponential decaying hopping and complex potentials as well as its dual model, which is just a non-Hermitian generalization of the Ganeshan-Pixley-Das Sarma model with nonreciprocal nearest-neighboring hopping. The presence of non-Hermitian term destroys the self-duality symmetry and thus prevents us exploring the localization-delocalization point through looking for self-dual points. Nevertheless, by applying Avila's global theory, the Lyapunov exponent of the Ganeshan-Pixley-Das Sarma model can be exactly derived, which enables us to get an analytical expression of mobility edge of the non-Hermitian dual model. Consequently, the mobility edge of the original model is obtained by using the dual transformation, which creates exact mappings between the spectra and wavefunctions of these two models.

arXiv comment9 pages, 3 figures

References in corpus (57)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Edge states and topological invariants of non-Hermitian systems
• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Localization transitions in non-Hermitian quantum mechanics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Topological phase transition in non-Hermitian quasicrystals
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• 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
• 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
• Non-Hermitian Delocalization and Eigenfunctions
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• One-dimensional quasicrystals with power-law hopping
• Majorana Fermions in superconducting 1D systems having periodic, quasiperiodic, and disordered potentials
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• 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
• Eigenvector statistics in non-Hermitian random matrix ensembles
• Photon propagation in a discrete fiber network: An interplay of coherence and losses
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Skin effect and winding number in disordered non-Hermitian systems
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• 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
• Observation of Bloch oscillations in complex PT-symmetric photonic lattices
• Non-Hermitian disorder in two-dimensional optical lattices
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential
• Anderson localization in the Non-Hermitian Aubry-André-Harper model with physical gain and loss
• Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
• Sharp Phase transitions for the almost Mathieu operator
• PT Symmetric Aubry-Andre Model
• Topological classification of defects in non-Hermitian systems
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• A Classification of Non-Hermitian Random Matrices
• Anderson Localization of cold atomic gases with effective spin-orbit interaction in a quasiperiodic optical lattice
• Localization Transition in Incommensurate non-Hermitian Systems
• The absolutely continuous spectrum of the almost Mathieu operator
• Non-Hermitian spectra and Anderson localization
• Localization problem of the quasiperiodic system with the spin orbit interaction
• Localization-delocalization transition in disordered systems with a direction
• Coexistence of zero Lyapunov exponent and positive Lyapunov exponent for new quasi-periodic Schr$\ddot{o}$dinger operator

Cited by in corpus (40)

• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Non-Hermitian skin effect and self-acceleration
• Critical phase dualities in 1D exactly-solvable quasiperiodic models
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals
• Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• Entanglement phase transitions in non-Hermitian quasicrystals
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Manipulating non-Hermitian skin effect via electric fields
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Non-Hermitian butterfly spectra in a family of quasiperiodic lattices
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Engineering mobility in quasiperiodic lattices with exact mobility edges
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Exponential size scaling of the Liouvillian gap in boundary-dissipated systems with Anderson localization
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Non-Hermitian topological mobility edges and transport in photonic quantum walks
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Coexistence of ergodic and weakly ergodic states in finite-height Wannier-Stark ladders
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Phase transitions in non-Hermitian superlattices
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Non-Hermitian off-diagonal disordered optical lattices
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• Family of self-dual quasicrystals with critical Phases
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals