Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems

Abstract

The Aubry-André-Harper (AAH) model with a self-dual symmetry plays an important role in studying the Anderson localization. Here we find a self-dual symmetry determining the quantum phase transition between extended and localized states in a non-Hermitian AAH model and show that the eigenenergies of these states are characterized by two types of winding numbers. By constructing and studying a non-Hermitian generalized AAH model, we further generalize the notion of the mobility edge, which separates the localized and extended states in the energy spectrum of disordered systems, to the non-Hermitian case and find that the generalized mobility edge is of a topological nature even in the open boundary geometry in the sense that the energies of localized and extended states exhibit distinct topological structures in the complex energy plane. Finally, we propose an experimental scheme to realize these models with electric circuits.

8 pages including supplementary materials

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Cited by in corpus (94)

• Non-Hermitian Physics
• Topological Non-Hermitian skin effect
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• 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
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Non-Hermitian skin effect and self-acceleration
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Floquet engineering of topological localization transitions and mobility edges in one-dimensional non-Hermitian quasicrystals
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Properties of the non-Hermitian SSH model: role of PT-symmetry
• Machine learning topological invariants of non-Hermitian systems
• Localization, $\mathcal{P}\mathcal{T}$-Symmetry Breaking and Topological Transitions in non-Hermitian Quasicrystals
• Non-Hermitian skin effects on many-body localized and thermal phases
• Non-Hermitian Maryland Model
• The fate of reentrant localization phenomenon in the one-dimensional dimerized quasiperiodic chain with long-range hopping
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Entanglement phase transitions in non-Hermitian quasicrystals
• Non-Hermitian skin effect edge
• Level statistics of real eigenvalues in non-Hermitian systems
• 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
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Universal non-Hermitian transport in disordered systems
• Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Damping transition in an open generalized Aubry-André-Harper model
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Power law hopping of single particles in one-dimensional non-Hermitian quasicrystals
• Topological triple phase transition in non-Hermitian quasicrystals with complex asymmetric hopping
• 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
• Non-Hermitian edge burst without skin localizations
• Universal characteristics of one-dimensional non-Hermitian superconductors
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Topological phonon polariton enhanced radiative heat transfer in bichromatic nanoparticle arrays mimicking Aubry-André-Harper model
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• From scale-free to Anderson localization: a size-dependent transition
• Interplay of nonreciprocity and nonlinearity on mean-field energy and dynamics of a Bose-Einstein condensate in a double-well potential
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• Robust Anderson transition in non-Hermitian photonic quasicrystals
• Long-range hopping in a quasiperiodic potential weakens the non-Hermitian skin effect
• Dynamical localization in non-Hermitian quasi-crystals
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Probing the superfluid-insulator phase transition by a non-Hermitian external field
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Universal hard-edge statistics of non-Hermitian random matrices
• Wannier-Stark localization in one-dimensional amplitude-chirped lattices
• Localization and topological transitions in generalized non-Hermitian SSH models
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Machine learning of mirror skin effects in the presence of disorder
• Exceptional Heavy-Fermion Semimetals in Three Dimensions
• Phase transitions in non-Hermitian superlattices
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Optimal spectral transport of non-Hermitian systems
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Localization with non-Hermitian off-diagonal disorder
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal