Non-Hermitian Boundary Modes

Abstract

We consider conditions for the existence of boundary modes in non-Hermitian systems with edges of arbitrary co-dimension. Through a universal formulation of formation criteria for boundary modes in terms of local Green functions, we outline a generic perspective on the appearance of such modes and generate corresponding dispersion relations. In the process, we explain the skin effect in both topological and non-topological systems, exhaustively generalizing bulk-boundary correspondence in the presence of non-Hermiticity. This is accomplished via a doubled Green's function, inspired by doubled Hamiltonian methods used to classify Floquet and, more recently, non-Hermitian topological phases. Our work constitutes a general tool, as well as, a unifying perspective for this rapidly evolving field. Indeed, as a concrete application we find that our method can expose novel non-Hermitian topological regimes beyond the reach of previous methods.

15 pages, 4 figures. Supplement added. Substantial extension of results

References in corpus (52)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Edge states and topological invariants of non-Hermitian systems
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Topological quantum chemistry
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Hermitian Chern bands
• 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
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Probing topological invariants in the bulk of a non-Hermitian optical system
• The space group classification of topological band insulators
• Topological Mott Insulators
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Topological classification of crystalline insulators through band structure combinatorics
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Topology of crystalline insulators and superconductors
• Edge states and topological phases in non-Hermitian systems
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Bulk-Boundary Correspondence in a Non-Hermitian System in One Dimension with Chiral-Inversion Symmetry
• Geometrical meaning of winding number and its characterization of topological phases in one-dimensional chiral non-Hermitian systems
• Periodic Table for Floquet Topological Insulators
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Topological states of non-Hermitian systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Simplified topological invariants for interacting insulators
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Anomalous helical edge states in a non-Hermitian Chern insulator
• Non-Hermitean Localization and De-Localization
• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• Knotted Non-Hermitian Metals
• Hall Conductance of a Non-Hermitian Chern Insulator
• Interplay between electronic topology and crystal symmetry: Dislocation-line modes in topological band-insulators
• Unified bulk-boundary correspondence for band insulators
• The translational side of topological band insulators
• Topological Amplification in Photonic Lattices
• Topological Bloch oscillations
• Dissolution of topological Fermi arcs in a dirty Weyl semimetal
• Topology and Observables of the Non-Hermitian Chern Insulator
• Self-organized pseudo-graphene on grain boundaries in topological band insulators
• Notes on topological insulators
• Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator
• Topological meaning of Z${}_2$ numbers in time reversal invariant systems

Cited by in corpus (578)

• Exceptional Topology of Non-Hermitian Systems
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• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Non-Hermitian Topology and Exceptional-Point Geometries
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Non-reciprocal robotic metamaterials
• Critical non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Reciprocal skin effect and its realization in a topolectrical circuit
• Non-Hermitian topological phenomena: A review
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Topological active matter
• Higher-order non-Hermitian skin effect
• Observation of higher-order non-Hermitian skin effect
• Observation of arbitrary topological windings of a non-Hermitian band
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• Topological Non-Hermitian skin effect
• Higher-order topological corner states induced by gain and loss
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Exponentially-enhanced quantum sensing with non-Hermitian lattice dynamics
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Knots and Non-Hermitian Bloch Bands
• Second-order topological non-Hermitian skin effects
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Non-Hermitian band topology and skin modes in active elastic media
• Topological Classification of Non-Hermitian Hamiltonians
• Perspective on topological states of non-Hermitian lattices
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
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• Skin effect and winding number in disordered non-Hermitian systems
• Geometric approach to fragile topology beyond symmetry indicators
• Non-Hermitian Edge Burst
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• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Simple formulas of directional amplification from non-Bloch band theory
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Non-Hermitian Dirac Cones
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• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Unraveling non-Hermitian pumping: emergent spectral singularities and anomalous responses
• Floquet Topological Phases of Non-Hermitian Systems
• Non-Hermitian second-order skin and topological modes
• Observation of exceptional points and skin effect correspondence in non-Hermitian phononic crystals
• Many-body topology of non-Hermitian systems
• Localization and topological transitions in non-Hermitian quasiperiodic lattices
• Experimental Realization of Weyl Exceptional Rings in a Synthetic Three-Dimensional Non-Hermitian Phononic Crystal
• Topology of anti-parity-time-symmetric non-Hermitian Su-Schrieffer-Heeger model
• Helical damping and anomalous critical non-Hermitian skin effect
• Bulk-boundary correspondence for non-Hermitian Hamiltonians via Green functions
• Hybrid skin-topological modes without asymmetric couplings
• Chirality as Generalized Spin-Orbit Interaction in Spintronics
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Many-body approach to non-Hermitian physics in fermionic systems
• Guided accumulation of active particles by topological design of a second-order skin effect
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Exceptional Topological Insulators
• Topological Field Theory of Non-Hermitian Systems
• Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Observation of non-Hermitian topology with non-unitary dynamics of solid-state spins
• Topological correspondence between magnetic space group representations
• Non-Hermitian fractional quantum Hall states
• Non-trivial point-gap topology and non-Hermitian skin effect in photonic crystals
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Many-Body Topological and Skin States without Open Boundaries
• Topological classification of non-Hermitian bands
• Non-Hermitian Many-Body Localization with Open Boundaries
• Symmetry classes of open fermionic quantum matter
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Non-Hermitian skin effect and self-acceleration
• Non-Hermitian skin clusters from strong interactions
• Liouvillian Skin Effect in an Exactly Solvable Model
• Review: Quantum Metrology and Sensing with Many-Body Systems
• Exceptional Bound States and negative Entanglement Entropy
• Experimental Realization of Geometry-Dependent Skin Effect in a Reciprocal Two-Dimensional Lattice
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Nonlinearity induced topological physics in momentum space and real space
• Topological Anderson insulators in two-dimensional non-Hermitian disordered systems
• Non-reciprocal transport of Exciton-Polaritons in a non-Hermitian chain
• Non-Bloch band theory in bosonic Bogoliubov-de Gennes systems
• Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice
• Dislocation Non-Hermitian Skin Effect
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Synthetic band-structure engineering in polariton crystals with non-Hermitian topological phases
• Hyperbolic Topological Band Insulators
• Non-Hermitian Bulk-Boundary Correspondence in Periodically Driven System
• Non-Hermitian Topological Phases: Principles and Prospects
• Detecting non-Bloch topological invariants in quantum dynamics
• Non-Hermitian Pseudo-Gaps
• Non-Hermitian skin effect beyond the tight-binding models
• Equivalence of the effective non-hermitian Hamiltonians in the context of open quantum systems and strongly-correlated electron systems
• Non-Hermitian Photonic Lattices: tutorial
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Non-Hermitian physics without gain or loss: the skin effect of reflected waves
• Ultrafast and Anharmonic Rabi Oscillations between Non-Bloch-Bands
• Accumulation of scale-free localized states induced by local non-Hermiticity
• Fate of Majorana zero modes, critical states and non-conventional real-complex transition in non-Hermitian quasiperiodic lattices
• Floquet second-order topological insulators in non-Hermitian systems
• Topological semimetal phase with exceptional points in one-dimensional non-Hermitian systems
• Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
• Dimensional transmutation from non-Hermiticity
• Exact solution of single impurity problem in non-reciprocal lattices: impurity induced size-dependent non-Hermitian skin effect
• Hermitian zero modes protected by nonnormality: Application of pseudospectra
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• Spectral deformations in non-Hermitian lattices with disorder and skin effect: a solvable model
• Non-Hermitian Topological Metamaterials with Odd Elasticity
• Non-Hermitian skin effect as an impurity problem
• Non-Hermitian band topology with generalized inversion symmetry
• Dual topological characterization of non-Hermitian Floquet phases
• Engineering Non-Hermitian Skin Effect with Band Topology in Ultracold Gases
• Non-Hermitian skin effect of dislocations and its topological origin
• Cascade of the delocalization transition in a non-Hermitian interpolating Aubry-Andr{é}-Fibonacci chain
• Non-Hermitian Mott Skin Effect
• Nielsen-Ninomiya Theorem with Bulk Topology: Duality in Floquet and Non-Hermitian Systems
• Non-Hermitian Floquet Topological Matter -- A Review
• Non-Hermitian generalizations of extended Su-Schrieffer-Heeger models
• Dynamical Degeneracy Splitting and Directional Invisibility in Non-Hermitian Systems
• Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems
• Curving the space by non-Hermiticity
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Non-Hermitian Chiral Skin Effect
• Dynamic winding number for exploring band topology
• Exceptional band touching for strongly correlated systems in equilibrium
• Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Designing non-Hermitian real spectra through electrostatics
• Topological aspects of periodically driven non-Hermitian Su-Schrieffer-Heeger model
• Non-Bloch band theory and bulk-edge correspondence in non-Hermitian systems
• Emergent entanglement phase transitions in non-Hermitian Aubry-André-Harper chains
• Unsupervised Learning of Non-Hermitian Topological Phases
• Zoology of non-Hermitian spectra and their graph topology
• A non-Hermitian optical atomic mirror
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems
• Biorthogonal quantum criticality in non-Hermitian many-body systems
• Sensitivity of non-Hermitian systems
• Topological origin of non-Hermitian skin effect in higher dimensions and uniform spectra
• Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase
• Scale-tailored localization and its observation in non-Hermitian electrical circuits
• Non-Hermitian strongly interacting Dirac fermions: a quantum Monte-Carlo study
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Topological Anderson insulators with different bulk states in quasiperiodic chains
• Non-Hermitian skin effect in magnetic systems
• Realization and Topological Properties of Third-Order Exceptional Lines Embedded in Exceptional Surfaces
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Geometry-dependent skin effects in reciprocal photonic crystals
• Non-Hermitian Squeezed Polarons
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Non-Hermitian dislocation modes: Stability and melting across exceptional points
• Loss-induced Floquet non-Hermitian skin effect
• Symmetry and topological classification of Floquet non-Hermitian systems
• Disorder-driven Phase Transitions of Second-order Non-Hermitian Skin Effects
• From the topological spin-Hall effect to the non-Hermitian skin effect in an elliptical micropillar chain
• Theoretical Prediction of Non-Hermitian Skin Effect in Ultracold Atom Systems
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Ring Structure in the Complex Plane: A Fingerprint of non-Hermitian Mobility Edge
• Untying links through anti-parity-time-symmetric coupling
• Bulk-boundary correspondence in point-gap topological phases
• Properties of the non-Hermitian SSH model: role of PT-symmetry
• Restoration of the non-Hermitian bulk-boundary correspondence via topological amplification
• Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm
• Topological origin of quantized transport in non-Hermitian Floquet chains
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Machine learning topological invariants of non-Hermitian systems
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Circuit realisation of a two-orbital non-Hermitian tight-binding chain
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
• Many-Body Non-Hermitian Skin Effect for Multipoles
• Nonreciprocal Charge and Spin Transport Induced by Non-Hermitian Skin Effect in Mesoscopic Heterojunctions
• Entanglement Spectrum Crossings Reveal non-Hermitian Dynamical Topology
• Topology in non-Hermitian Chern insulators with skin effect
• Kubo formula for non-Hermitian systems and tachyon optical conductivity
• Boundary Condition Independence of Non-Hermitian Hamiltonian Dynamics
• Entanglement Entropy of Non-Hermitian Free Fermions
• Non-Hermitian skin effects on many-body localized and thermal phases
• Non-Hermitian Maryland Model
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• Non-Hermitian Absorption Spectroscopy
• Hermitian and Non-Hermitian Topology from Photon-Mediated Interactions
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• R-DMFT study of a non-Hermitian skin effect for correlated systems: analysis based on a pseudo-spectrum
• Topological phases protected by shifted sublattice symmetry in dissipative quantum systems
• Non-Bloch quench dynamics
• Exceptional points make an astroid in non-Hermitian Lieb lattice: evolution and topological protection
• Dynamic skin effects in non-Hermitian systems
• Universal platform of point-gap topological phases from topological materials
• Cyclotron quantization and mirror-time transition on nonreciprocal lattices
• Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect
• Topological invariants, zero mode edge states and finite size effect for a generalized non-reciprocal Su-Schrieffer-Heeger model
• Compatibility of transport effects in non-Hermitian nonreciprocal systems
• Unraveling the topology of dissipative quantum systems
• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Non-Hermitian boundary spectral winding
• General corner states in 2D SSH model with intracelluar next-nearest-neighbour hopping
• Exceptional points in the one-dimensional Hubbard model
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Continuum of Bound States in a Non-Hermitian Model
• The topological counterparts of non-Hermitian SSH models
• Solvable non-Hermitian skin effect in many-body unitary dynamics
• Amplification of quantum signals by the non-Hermitian skin effect
• Non-Hermitian skin effect edge
• Diagnosis of bulk phase diagram of non-reciprocal topological lattices by impurity modes
• Topology of multipartite non-Hermitian one-dimensional systems
• Manipulating non-Hermitian skin effect via electric fields
• Topological continuum charges of acoustic phonons in 2D
• Bound states and photon emission in non-Hermitian nanophotonics
• Exponentially growing bulk Green functions as signature of nontrivial non-Hermitian winding number in one dimension
• A Non-Hermitian Moiré Valley Filter
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Anatomy of open-boundary bulk in multiband non-Hermitian systems
• Protection of parity-time symmetry in topological many-body systems: non-Hermitian toric code and fracton models
• Topological enhancement of non-normality in non-Hermitian skin effects
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Dissipative analog of four-dimensional quantum Hall physics
• Double exceptional links in a three-dimensional dissipative cold atomic gas
• Erratic non-Hermitian skin localization
• Dynamical robustness of topological end states in nonreciprocal Su-Schrieffer-Heeger models with open boundary conditions
• Bridging the gap between topological non-Hermitian physics and open quantum systems
• Stochastic non-Hermitian skin effect
• Giant Emitters in a Structured Bath with Non-Hermitian Skin Effect
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Mixed higher-order topology: boundary non-Hermitian skin effect induced by a Floquet bulk
• Non-Hermitian topological end breathers
• Observation of scale-free localized states induced by non-Hermitian defects
• Edge theory of non-Hermitian skin modes in higher dimensions
• Non-Hermitian Weyl semimetal and its Floquet engineering
• Direction reversal of non-Hermitian skin effect via coherent coupling
• The Bulk-boundary Correspondence in Non-Hermitian Hopf-link Exceptional Line Semimetals
• Dynamical scaling of Loschmidt echo in non-Hermitian systems
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Geometry and superfluidity of the flat band in a non-Hermitian optical lattice
• Non-Hermitian topology in rock-paper-scissors games
• A brief review of hybrid skin-topological effect
• Quantum dynamics on a lossy non-Hermitian lattice
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Degeneracy and defectiveness in non-Hermitian systems with open boundary
• Engineering Dissipative Quasicrystals
• Green's functions of multiband non-Hermitian systems
• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Universal scalefree non-Hermitian skin effect near the Bloch point
• The bosonic skin effect: boundary condensation in asymmetric transport
• Absence of logarithmic and algebraic scaling entanglement phases due to skin effect
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Fate of exceptional points under interactions: Reduction of topological classifications
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Absence of measurement-induced entanglement transition due to feedback-induced skin effect
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Non-Hermitian Topology in Hermitian Topological Matter
• The non-Hermitian skin effect: A perspective
• Two-dimensional quantum walk with non-Hermitian skin effects
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Non-Hermitian Skin Effect in Periodically-Driven Dissipative Ultracold Atoms
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Non-Hermitian impurities in Dirac systems
• Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence
• Irrational Non-Abelian Statistics for Non-Hermitian Generalization of Majorana Zero Modes
• Non-linear dynamics of the non-Hermitian Su-Schrieffer-Heeger model
• Machine learning non-Hermitian topological phases
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Degeneracies and symmetry breaking in pseudo-Hermitian matrices
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Damping transition in an open generalized Aubry-André-Harper model
• Rational Approximations of Quasi-Periodic Problems via Projected Green's Functions
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Non-Bloch band theory of generalized eigenvalue problems
• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
• Statistical mechanics for non-Hermitian quantum systems
• Non-Hermitian Floquet phases with even-integer topological invariants in a periodically quenched two-leg ladder
• Topological characterization of non-Hermitian multiband systems using Majorana's Stellar Representation
• Non-Abelian Braiding of Topological Edge Bands
• Geometry-dependent skin effect and anisotropic Bloch oscillations in a non-Hermitian optical lattice
• Evidencing non-Bloch dynamics in temporal topolectrical circuits
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Exact formulas of the end-to-end Green's functions in non-Hermitian systems
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Real spectra, Anderson localization, and topological phases in one-dimensional quasireciprocal systems
• Topological properties of a non-Hermitian quasi-1D chain with a flat band
• Non-Hermitian spectral flows and Berry-Chern monopoles
• Critical non-Hermitian topology induced quantum sensing
• Making topologically trivial non-Hermitian systems nontrivial via gauge fields
• Characterizing the Bulk-Boundary Correspondence of one-dimensional non-Hermitian interacting systems by edge entanglement entropy
• Quantum criticality in interacting bosonic Kitaev-Hubbard models
• Observation of size-dependent boundary effects in non-Hermitian electric circuits
• Correlation effects on non-Hermitian point-gap topology in zero dimension: reduction of topological classification
• Non-Hermitian topological exciton-polariton corner modes
• Non-Hermitian edge burst without skin localizations
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Non-Hermiticity induced Exceptional Points and Skin Effect in the Dice-Haldane Model
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Algebraic non-Hermitian skin effect and generalized Fermi surface formula in arbitrary dimensions
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Filling up complex spectral regions through non-Hermitian disordered chains
• Localization via Quasi-Periodic Bulk-Bulk Correspondence
• Chiral metals and entrapped insulators in a one-dimensional topological non-Hermitian system
• Non-Hermitian second-order topological superconductors
• Kramers' degeneracy for open systems in thermal equilibrium
• Topological superconductivity enhanced by exceptional points
• Scaling laws for non-Hermitian skin effect with long-range couplings
• Non-Hermitian topological ohmmeter
• Many-body Non-Hermitian Skin Effect At Finite Temperatures
• The simulation of non-Hermitian disordered system in linear circuits
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Characterizing and Tuning Exceptional Points Using Newton Polygons
• Exponentially Enhanced non-Hermitian Cooling
• Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Non-Hermitian topological phases and skin effects in kagome lattices
• Observation of disorder-induced boundary localization
• Non-Hermitian higher-Order Weyl semimetal with surface diabolic points
• Non-Hermitian Avalanche Effect: Non-Perturbative Effect Induced by Local Non-Hermitian Perturbation on a Z2 Topological Order
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Driven-dissipative topological phases in parametric resonator arrays
• Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{P}\mathcal{T}$ symmetric non-Hermitian system by using non-unitary quantum walks
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Construction of Non-Hermitian Parent Hamiltonian from Matrix Product States
• Pseudomagnetic suppression of non-Hermitian skin effect
• Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
• Two-dimensional anisotropic non-Hermitian Lieb lattice
• Many-body entanglement and spectral clusters in the extended hard-core bosonic Hatano-Nelson model
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Alice string in Non-Hermitian Systems
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Identifying gap-closings in open non-Hermitian systems by Biorthogonal Polarization
• Point-Gap Bound States in Non-Hermitian Systems
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Evolution of spectral topology in one-dimensional long-range nonreciprocal lattices
• Topology of multiple cross-linked Su-Schrieffer-Heeger chains
• Dynamical signatures of point-gap Weyl semimetal
• Boundary sensitive Lindbladians and relaxation dynamics
• Topology of rotating stratified fluids with and without background shear flow
• Many-body phase transitions in a non-Hermitian Ising chain
• Symmetric non-Hermitian skin effect with emergent nonlocal correspondence
• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Hermitian Topologies originating from non-Hermitian braidings
• Unravelling the edge spectra of non-Hermitian Chern insulators
• Nontrivial worldline winding in non-Hermitian quantum systems
• Giant non-reciprocity and gyration through modulation-induced Hatano-Nelson coupling in integrated photonics
• Real-space topological localizer index to fully characterize the dislocation skin effect
• Gain/loss effects on spin-orbit coupled ultracold atoms in two-dimensional optical lattices
• Observation of non-local impedance response in a passive electrical circuit
• Anomalous dynamical response of non-Hermitian topological phases
• Non-Hermitian BCS-BEC crossover of Dirac fermions
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Topological quantum optical states in quasiperiodic cold atomic chains
• Selective and tunable excitation of topological non-Hermitian skin modes
• Multifractality of many-body non-Hermitian skin effect
• Protection of all nondefective twofold degeneracies by anti-unitary symmetries in non-Hermitian systems
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Floquet Exceptional Topological Insulator
• Nonlinear perturbation of a high-order exceptional point: skin discrete breathers and the hierarchical power-law scaling
• Imaginary gap-closed points and dynamics in a class of dissipative systems
• Direct observation of energy band attraction effect in non-Hermitian systems
• Quantum-Classical Correspondence of Non-Hermitian Symmetry Breaking
• Role of Topology in Relaxation of One-Dimensional Stochastic Processes
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Fundamental constraints on the observability of non-Hermitian effects in passive systems
• Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
• Discriminant indicators with generalized inversion symmetry
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Information constraint in open quantum systems
• Extended imaginary gauge transformation in a general nonreciprocal lattice
• Complex semiclassical theory for non-Hermitian quantum systems
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Equivalence and superposition of real and imaginary quasiperiodicities
• Dynamical signatures of the Yang-Lee edge singularity in non-Hermitian systems
• Concentrated subradiant modes in one-dimensional atomic array coupled with chiral waveguides
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Universal spectral moment theorem and its applications in non-Hermitian systems
• Tailoring Bound State Geometry in High-Dimensional Non-Hermitian Systems
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Non-Hermitian Quantum Fractals
• Photon-mediated dipole-dipole interactions as a resource for quantum science and technology in cold atoms
• Interaction-Induced Second-Order Skin Effect
• Non-Floquet engineering in periodically driven non-Hermitian systems
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Non-Hermitian semi-Dirac semi-metals
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Edge states in a non-Hermitian topological crystalline insulator
• Braids and Higher-order Exceptional Points from the Interplay Between Lossy Defects and Topological Boundary States
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Non-Bloch dynamics and topology in a classical non-equilibrium process
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Topological characterization of a non-Hermitian ladder via Floquet non-Bloch theory
• Real spectra in one-dimensional single-band non-Hermitian Hamiltonians
• Localization and mobility edges in non-Hermitian continuous quasiperiodic systems
• Non-Hermitian skin effect and lasing of absorbing open-boundary modes in photonic crystals
• Chiral-Extended Photon-Emitter Dressed States in Non-Hermitian Topological Baths
• Exceptional magic angles in non-Hermitian twisted bilayer graphene
• Non-Hermitian generalizations of the Yao-Lee model augmented by SO(3)-symmetry-breaking terms
• General theory for infernal points in non-Hermitian systems
• Entangelment Entropy on Generalized Brillouin Zone
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Coexistence of non-Hermitian skin effect and extended states in one-dimensional nonreciprocal lattices
• Complete absorption of topologically protected waves
• Localization and topological transitions in generalized non-Hermitian SSH models
• Field Theoretical Study of Disorder in Non-Hermitian Topological Models
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• Lindbladian versus Postselected Non-Hermitian Topology
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Electronic polarization in non-Bloch band theory
• Berry curvature inside parity-time-symmetry protected exceptional surface
• Topological phase transition in fluctuating imaginary gauge fields
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Non-Bloch Dirac Points and Phase Diagram in the Stacked Non-Hermitian SSH Model
• Delocalization of skin steady states
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Formal Green's function theory in non-Hermitian lattice systems
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Non-reciprocity is necessary for robust dimensional reduction and strong responses in stochastic topological systems
• Parsing skin effect in a non-Hermitian spinless BHZ-like model
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Anomalous hybridization of spectral winding topology in quantized steady-state responses
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Fidelity and criticality in the nonreciprocal Aubry-Andr{é}-Harper model
• Restoration of non-Hermitian bulk-boundary correspondence by counterbalancing skin effect
• Two-dimensional lattice with an imaginary magnetic field
• Topology of Discrete Quantum Feedback Control
• One-dimensional non-Hermitian band structures as Riemann surfaces
• Spin-dependent gain and loss in photonic quantum spin Hall systems
• Exponential quantum advantages for practical non-Hermitian eigenproblems
• Emergent Non-Hermitian Edge Polarisation in an Hermitian Tight-binding Model
• Many-body critical non-Hermitian skin effect
• Topological directed amplification
• Emergent non-Hermitian physics in generalized Lotka-Volterra model
• Machine learning of mirror skin effects in the presence of disorder
• Real-time edge dynamics of non-Hermitian lattices
• Yang-Lee edge singularity and quantum criticality in non-Hermitian PXP model
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Inverse Design of Winding Tuple for Non-Hermitian Topological Edge Modes
• Extended unitarity and absence of skin effect in periodically driven systems
• Loss-induced universal one-way transport in periodically driven systems
• Composite Quantum Phases in Non-Hermitian Systems
• Duality between Generalized Non-Hermitian HN Model in Flat Space and Hermitian System in Curved space
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Discriminant indicator with generalized rotational symmetry
• Renormalization approach to the analysis and design of Hermitian and non-Hermitian interfaces
• Optical non-Hermitian skin effect in two-dimensional uniform media
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors
• Winding Topology of Multifold Exceptional Points
• Entanglement Spectrum Dynamics as a Probe for Non-Hermitian Bulk-Boundary Correspondence in Systems with Periodic Boundaries
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Exceptional second-order topological insulators
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Chiral Dissociation of Bound Photon Pairs for a Non-Hermitian Skin Effect
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Theory for the spectral splitting exponent of exceptional points
• Quantum Pontus-Mpemba Effect Enabled by the Liouvillian Skin Effect
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions
• Topological split-ring resonator based metamaterials with $\mathcal{P}\mathcal{T}$ symmetry relying on gain and loss
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Selective branching, quenching, and converting of topological modes
• Phase Diagram of a Non-Hermitian Chern Insulator: Destabilization of Chiral Edge States and Bulk-Boundary Correspondence
• Alternating quantum-emitter chains: Exceptional-point phase transition, edge state, and quantum walks
• Hermitian and non-Hermitian topology in active matter
• Topological phases of many-body non-Hermitian systems
• Gauge Field Induced Unconventional Skin Effect in Spinful Non-Hermitian Systems
• Non-Hermitian tearing by dissipation
• Dissolution of the non-Hermitian skin effect in one-dimensional lattices with linearly varying nonreciprocal hopping
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Band structures under non-Hermitian periodic potentials: Connecting nearly-free and bi-orthogonal tight-binding models
• Non-Hermitian Multipole Skin Effects Challenge Localization
• Controllable suppression of Non-Hermitian skin effects
• Bulk--Boundary Correspondence and Boundary Zero Modes in a Non-Hermitian Kitaev Chain Model
• Exact multiple complex mobility edges and quantum state engineering in coupled 1D quasicystals
• From Hermitian critical to non-Hermitian point-gapped phases
• Nonequilibrium electron distribution function in a voltage-biased nanowire: A nonequilibrium Green's function approach
• Non-Hermitian Hopf insulators
• Experimental observation of energy-band Riemann surface
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Topological and fractal defect states in non-Hermitian lattices
• Band topology of pseudo-Hermitian phases through tensor Berry connections and quantum metric
• From Chiral Topological Dynamics to Chiral Topological Amplification: Real vs Imaginary Parameters in a Hermitian Bosonic Chain
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• 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
• Measuring topological invariants of even-dimensional line-gapped non-Hermitian systems through quench dynamics
• High-fidelity multipartite entanglement creation in non-Hermitian qubits
• The quantum phase transitions of dimer chain driven by an imaginary ac field
• PT-symmetric Non-Hermitian Hopf Metal
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Anti-parity-time topologically undefined state
• Scattering Dynamics and Boundary States of a Non-Hermitian Dirac Equation
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Topological Amplification of the Bosonic Kitaev Chain with Non-Uniform Loss
• Gaussian eigenstate pinning in non-Hermitian quantum mechanics
• Optimal spectral transport of non-Hermitian systems
• Inter-species topological phases via a dynamical gauge field
• Interplay of Disorder and Point-Gap Topology: Chiral Modes, Localization and Non-Hermitian Anderson Skin Effect in One Dimension
• Dynamical non-Hermitian systems: Fingerprints and pure dephasing induced protection effect
• Floquet Non-Bloch Formalism for a Non-Hermitian Ladder: From Theoretical Framework to Topolectrical Circuits
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Entanglement manifestation of knot topology in a non-Hermitian lattice
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Magnetic Control of the Non-Hermitian Skin Effect in Two-Dimensional Lattices
• Minimal Hamiltonian deformations as bulk probes of effective non-Hermiticity in Dirac materials
• Tailoring Corner States and Exceptional Points in Altermagnets
• Tailoring higher-order van Hove singularities in non-Hermitian interface systems via Floquet engineering
• Real spectra and phase transition of skin effect in nonreciprocal systems
• Quantum-vacuum-protected topological edge polaritons
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Emergence of Hermitian topology from non-Hermitian knots
• Supermetal-insulator transition in a non-Hermitian network model
• Recurrence method in Non-Hermitian Systems
• Non-Hermitian Higher-Order Weyl Semimetals
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems
• Self-healing of non-Hermitian topological skin modes
• Topology of the simplest gene switch
• Observation of non-Hermitian point gap in photonic crystals
• Covariant formulation of the Berry connection in non-Hermitian systems
• Non-Hermitian Higher-Order Dirac Semimetals
• Illuminating the bulk-boundary correspondence of a non-Hermitian stub lattice with Majorana stars
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Coexistence of topological Anderson insulator and multifractal critical phase in a non-Hermitian quasicrystal
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals
• Simulating monitoring-induced topological phase transitions with small systems
• Fate of Majorana zero modes by a modified real-space-Pfaffian method and mobility edges in a one-dimensional quasiperiodic lattice
• Anomalous Point-Gap Interactions Unveil the Mirage Bath
• Topological Classification of Gapped/Gap-preserving Rational Space-Time Crystal Systems
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Anomalous Transport Induced by Non-Hermitian Anomalous Berry Connection in Non-Hermitian Systems
• Algebraic States in Continuum in $d>1$ Dimensional Non-Hermitian Systems
• Physical constraints on effective non-Hermitian systems
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Anatomy of Non-Hermitian Dynamical Quantum Phase Transitions
• Winding-control mechanism of non-Hermitian systems
• Zero Indirect Band Gap in Non-Hermitian Systems
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Interacting many-body non-Hermitian systems as Markov chains
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Topology of the generalized Brillouin zone of one-dimensional models