Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points

Abstract

Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward an ordering unique to non-Hermitian lattices, whereby a pristine system becomes devoid of extended states, a property which turns out to be robust to disorder. This is enabled by a peculiar type of non-Hermitian degeneracy where a macroscopic fraction of the states coalesce at a single point with geometrical multiplicity of $1$, that we call a phenomenal point.

6 pages, 4 figures

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• Information constraint in open quantum systems
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• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
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• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
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• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
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• Topological states at exceptional points
• Nonlinear Hall effects with an exceptional ring
• Generalized topological bulk-edge correspondence in bulk-Hermitian continuous systems with non-Hermitian boundary conditions
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Emergent localized states at the interface of a twofold $\mathcal{P}\mathcal{T}$-symmetric lattice
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Equilibrium states in open quantum systems
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Exceptional stationary state in a dephasing many-body open quantum system
• Liouvillian skin effect in quantum neural networks
• Non-Quantized Edge Channel Conductance and Zero Conductance Fluctuation in Non-Hermitian Chern Insulators
• Many-body critical non-Hermitian skin effect
• Loss-induced universal one-way transport in periodically driven systems
• Topologically compatible non-Hermitian skin effect
• Machine learning of mirror skin effects in the presence of disorder
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Phase transitions as a manifestation of spontaneous unitarity violation
• Topological directed amplification
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Extended unitarity and absence of skin effect in periodically driven systems
• Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
• Topological, multi-mode amplification induced by non-reciprocal, long-range dissipative couplings
• Exceptional second-order topological insulators
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Tentaclelike spectra and bound states in Hatano-Nelson chain with long-range impurity coupling
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Winding Topology of Multifold Exceptional Points
• Chiral Dissociation of Bound Photon Pairs for a Non-Hermitian Skin Effect
• Classical-quantum correspondence for two-level pseudo-Hermitian systems
• Discriminant indicator with generalized rotational symmetry
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Topological phases of many-body non-Hermitian systems
• Defect-driven incoherent skin localization
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Non-Hermitian tearing by dissipation
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Random non-Hermitian action theory for stochastic quantum dynamics: from canonical to path integral quantization
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• How to realize compact and non-compact localized states in disorder-free hypercube networks
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• Meissner effect in non-Hermitian superconductors
• Coherent transfer of topological domain walls
• Random non-Hermitian Hamiltonian framework for symmetry breaking dynamics
• Exceptional Points, Bulk-Boundary Correspondence, and Entanglement Properties for a Dimerized Hatano-Nelson Model with Staggered Potentials
• High-fidelity multipartite entanglement creation in non-Hermitian qubits
• Symmetry-induced fragmentation and dissipative time crystal
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Non-Hermitian Hopf insulators
• Nonequilibrium protection effect and spatial localization of noise-induced fluctuations: Quasi-one-dimensional driven lattice gas with partially penetrable obstacle
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Exceptional mode topological surface laser
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• PT-symmetric Non-Hermitian Hopf Metal
• Exceptional points in SSH-like models with hopping amplitude gradient
• Topological spin textures in electronic non-Hermitian systems
• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
• Uncovering Exceptional Contours in non-Hermitian Hyperbolic Matter
• Quantum phase transitions mediated by clustered non-Hermitian degeneracies
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Topological and fractal defect states in non-Hermitian lattices
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Adiabatic charge transport through non-Bloch bands
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Non-Hermitian higher-order topological insulators enabled by altermagnet engineering
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Tailoring Corner States and Exceptional Points in Altermagnets
• Inter-species topological phases via a dynamical gauge field
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Non-Hermitian topology of transport in the quantum Hall phases in graphene
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Scaling of pseudospectra in exponentially sensitive lattices
• Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Topology and $\mathcal{P}\mathcal{T}$ Symmetry in a Non-Hermitian Su-Schrieffer-Heeger Chain with Periodic Hopping Modulation
• Disorder and non-Hermiticity in Kitaev spin liquids with a Majorana Fermi surface
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Noisy Stark probes as quantum-enhanced sensors
• Scattering Dynamics and Boundary States of a Non-Hermitian Dirac Equation
• Topological invariant of velocity field in quantum systems
• Quantum-vacuum-protected topological edge polaritons
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Anomalous reflection at the interface of binary synthetic photonic lattices
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Correspondence between non-Hermitian topology and directional amplification in the presence of disorder
• Dynamic manifestation of exception points in a non-Hermitian continuous model with an imaginary periodic potential
• Topology of the generalized Brillouin zone of one-dimensional models
• Winding-control mechanism of non-Hermitian systems
• $\mathcal{P}\mathcal{T}$-Symmetric Spin--Boson Model with a Continuous Bosonic Spectrum: Exceptional Points and Dynamics
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Anomalous Non-Hermitian Topological Anderson Insulator
• Precision-Induced Irreversibility in non-Hermitian systems
• $q$th-root non-Hermitian Floquet topological insulators
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Robust interface-state laser in non-Hermitian micro-resonator arrays
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Emulating non-Hermitian dynamics in a finite non-dissipative quantum system
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Self-healing of non-Hermitian topological skin modes
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Reversing non-Hermitian skin accumulation with a non-local transverse switch
• Non-Hermitian Higher-Order Dirac Semimetals
• Exceptional flat bands in bipartite non-Hermitian lattices
• Supercharging exceptional points: Full-spectrum pairwise coalescence in non-Hermitian systems
• Hall conductance of a non-Hermitian two-band system with k-dependent decay rates