Non-Hermitian Delocalization and Eigenfunctions

Abstract

Recent literature on delocalization in non-Hermitian systems has stressed criteria based on sensitivity of eigenvalues to boundary conditions and the existence of a non-zero current. We emphasize here that delocalization also shows up clearly in eigenfunctions, provided one studies the product of left- and right-eigenfunctions, as required on physical grounds, and not simply the squared modulii of the eigenfunctions themselves. We also discuss the right- and left-eigenfunctions of the ground state in the delocalized regime and suggest that the behavior of these functions, when considered separately, may be viewed as ``intermediate'' between localized and delocalized.

8 pages, 11 figures included

References in corpus (5)

• Winding Numbers, Complex Currents, and Non-Hermitian Localization
• Random Dirac Fermions and Non-Hermitian Quantum Mechanics
• Localization in non-Hermitian quantum mechanics and flux-line pinning in superconductors
• A Non-Hermitean Particle in a Disordered World
• Finite Size Effects in Vortex Localization

Cited by in corpus (196)

• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Non-Bloch Band Theory of Non-Hermitian Systems
• Edge states and topological phases in non-Hermitian systems
• Critical non-Hermitian Skin Effect
• Topological phase transition in non-Hermitian quasicrystals
• Classification of Exceptional Points and Non-Hermitian Topological Semimetals
• Non-Hermitian Many-Body Localization
• Topological states of non-Hermitian systems
• Robust light transport in non-Hermitian photonic lattices
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Non-Hermitian transparency and one-way transport in low-dimensional lattices by an imaginary gauge field
• Skin effect and winding number in disordered non-Hermitian systems
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• 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 mobility edges in one-dimensional quasicrystals with parity-time symmetry
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Phase transitions in a non-Hermitian Aubry-André-Harper model
• Complex Skin Modes in Non-Hermitian Coupled Laser Arrays
• Non-Hermitian Many-Body Localization with Open Boundaries
• Explicit definition of $\mathcal{P}\mathcal{T}$ symmetry for non-unitary quantum walks with gain and loss
• Liouvillian Skin Effect in an Exactly Solvable Model
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Statistical properties of eigenvectors in non-Hermitian Gaussian random matrix ensembles
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Dislocation Non-Hermitian Skin Effect
• Transport and spectral features in non-Hermitian open systems
• Bound states, scattering states and resonant states in PT-symmetric open quantum systems
• Non-Hermitian skin effect beyond the tight-binding models
• Violation of detailed balance accelerates relaxation
• Electric-circuit simulation of the Schrödinger equation and non-Hermitian quantum walks
• 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
• Interaction-induced non-Hermitian topological phases from a dynamical gauge field
• Curving the space by non-Hermiticity
• Exceptional band touching for strongly correlated systems in equilibrium
• Dynamical nonlinear higher-order non-Hermitian skin effects and topological trap-skin phase
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Non-Hermitian bidirectional robust transport
• Zoology of non-Hermitian spectra and their graph topology
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Sensitivity of non-Hermitian systems
• Unusual wave-packet spreading and entanglement dynamics in non-Hermitian disordered many-body systems
• Fate of zero modes in a finite Su-Schrieffer-Heeger Model with $\mathcal{P}\mathcal{T}$ Symmetry
• Non-Hermitian Aubry-André model with Power-Law Hopping
• Non-Hermitian Squeezed Polarons
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Connections between the Open-boundary Spectrum and Generalized Brillouin Zone in Non-Hermitian Systems
• Anderson localization transition in a robust $\mathcal{P}\mathcal{T}$-symmetric phase of a generalized Aubry-Andre model
• Spectral Properties of Disordered Interacting Non-Hermitian Systems
• Gain/loss induced localization in one-dimensional PT-symmetric tight-binding models
• Diagnosing non-Hermitian Many-Body Localization and Quantum Chaos via Singular Value Decomposition
• Topology in non-Hermitian Chern insulators with skin effect
• Non-Hermitian Stark Many-Body Localization
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Localization-delocalization transition in disordered systems with a direction
• Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Universal platform of point-gap topological phases from topological materials
• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Bloch oscillations in non-Hermitian lattices with trajectories in complex plane
• Non-Hermitian pseudo mobility edge in a coupled chain system
• Skin modes in a nonlinear Hatano-Nelson model
• Landau-Zener-Stückelberg Interferometry in $\mathcal{P}\mathcal{T}$-symmetric Non-Hermitian models
• Exact Mobility Edges and Topological Phase Transition in Two-Dimensional non-Hermitian Quasicrystals
• Manipulating non-Hermitian skin effect via electric fields
• Topological enhancement of non-normality in non-Hermitian skin effects
• Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss
• Stochastic non-Hermitian skin effect
• Erratic non-Hermitian skin localization
• Non-Hermitean Random Matrix Theory: Summation of Planar Diagrams, the "Single-Ring" Theorem and the Disk-Annulus Phase Transition
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Entanglement dynamics in the many-body Hatano-Nelson model
• Delocalization in an open one-dimensional chain in an imaginary vector potential
• Anderson transition at complex energies in one-dimensional parity-time-symmetric disordered systems
• Tight-binding lattices with an oscillating imaginary gauge field
• Controllable unidirectional transport and photon storage in an one-dimensional lattice with complex hopping rates
• Point-gap topology with complete bulk-boundary correspondence in dissipative quantum systems
• Exact description of coalescing eigenstates in open quantum systems in terms of microscopic Hamiltonian dynamics
• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Non-hermitian exciton dynamics in a photosynthetic unit system
• Dynamics of Molecular Motors with Finite Processivity on Heterogeneous Tracks
• Anderson Delocalization in Strongly Coupled Disordered Non-Hermitian Chains
• Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach
• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Eigenvalue Repulsion and Eigenfunction Localization in Sparse Non-Hermitian Random Matrices
• Loschmidt echo and fidelity decay near an exceptional point
• Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences
• Statics and Dynamics of non-Hermitian Many-Body Localization
• Damping transition in an open generalized Aubry-André-Harper model
• PT phase transition in a (2+1)-d relativistic system
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• QT-Symmetry and Weak Pseudo-Hermiticity
• Spectral analysis of electron transfer kinetics II
• Emergent conservation in Floquet dynamics of integrable non-Hermitian models
• Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
• Scaling laws for non-Hermitian skin effect with long-range couplings
• Exploring the impact of fluctuation-induced criticality on non-hermitian skin effect and quantum sensors
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• Spectral structure and doublon dissociation in the two-particle non-Hermitian Hubbard model
• Robust quantum boomerang effect in non-Hermitian systems
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Non-Hermitian Fabry-Perot Resonances in a PT-symmetric system
• From Ergodicity to Many-Body Localization in a One-Dimensional Interacting Non-Hermitian Stark System
• Hatano-Nelson model with a periodic potential
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Ubiquity of the quantum boomerang effect in Hermitian Anderson-localized systems
• Coherent states of non-Hermitian quantum systems
• Synthetic Mechanical Lattices with Synthetic Interactions
• Localization-Delocalization Transitions in Non-Hermitian Aharonov-Bohm Cages
• Giant non-reciprocity and gyration through modulation-induced Hatano-Nelson coupling in integrated photonics
• Vortices in a cylinder: Localization after depinning
• The particle in a box in PT quantum mechanics and an electromagnetic analog
• Population Dynamics and Non-Hermitian Localization
• Coexistence of stable and unstable population dynamics in a nonlinear non-Hermitian mechanical dimer
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Kibble-Zurek scaling in one-dimensional localization transitions
• Interaction effects in non-Hermitian models of vortex physics
• Entanglement transitions in a periodically driven non-Hermitian Ising chain
• Fate of Topological Edge States in Disordered Periodically-driven Nonlinear Systems
• Two-dimensional Non-Hermitian Delocalization Transition as a Probe for the Localization Length
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Striated Populations in Disordered Environments with Advection
• Non-Hermitian control of localization in mosaic photonic lattices
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Detecting bulk and edge exceptional points in non-Hermitian systems through generalized Petermann factors
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Magnetic Flux Response of Non-Hermitian Topological Phases
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Hilbert space fragmentation imposed real spectrum of non-Hermitian systems
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• Complex magnetic fields: An improved Hardy-Laptev-Weidl inequality and quasi-self-adjointness
• General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• Harnessing Nonlinearity to Tame Wave Dynamics in Nonreciprocal Active Systems
• Anyonic $\mathcal{P}\mathcal{T}$ symmetry, drifting potentials and non-Hermitian delocalization
• Unveiling Eigenstate Thermalization for Non-Hermitian systems
• Topological Invariant for Multi-Band Non-hermitian Systems with Chiral Symmetry
• Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
• Abnormal Frequency Response Determined by Saddle Points in Non-Hermitian Crystal Systems
• Phase diagram of non-Hermitian BCS superfluids in a dissipative asymmetric Hubbard model
• Nonlinear Hall effects with an exceptional ring
• Quantum Sensing with Driven-Dissipative Su-Schrieffer-Heeger Lattices
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Reconfiguration of quantum states in $\mathcal{P}T$-symmetric quasi-one dimensional lattices
• The Consequences of Non-Normality
• "Lifshitz tails" and extended states in an Imaginary random potential
• Localization of Lindbladian Fermions
• Probing localization properties of many-body Hamiltonians via an imaginary vector potential
• Boundary-driven many-body phase transitions in a non-Hermitian disordered fermionic chain
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Extended unitarity and absence of skin effect in periodically driven systems
• Topology of Discrete Quantum Feedback Control
• Quantum feedback induced entanglement relaxation and dynamical phase transition in monitored free fermion chains with Wannier-Stark ladder
• Spin-Depairing-Induced Exceptional Fermionic Superfluidity
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• Nonlinear skin breathing modes in one-dimensional nonreciprocal mechanical lattices
• Phase transitions in non-Hermitian superlattices
• Finite steady-state current defies non-Hermitian many-body localization
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Fate of localization features in a one-dimensional non-Hermitian flat-band lattice with quasiperiodic modulations
• Eigenvalue spectral tails and localization properties of asymmetric networks
• Non-Hermitian Delocalization Induced by Residue Imaginary Velocity
• Non-Hermitian Multipole Skin Effects Challenge Localization
• A non-Hermitian Su-Schrieffer-Heeger model with the energy levels of free parafermions
• From Hermitian critical to non-Hermitian point-gapped phases
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Emergent tilt order in Dirac polymer liquids
• Wave propagation in an elastic lattice with non-reciprocal stiffness and engineered damping
• Markov generators as non-hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and Singular Value Decompositions
• Exceptional points in SSH-like models with hopping amplitude gradient
• Theory of Localization in a Disordered Ring in a Non-Hermitian Field
• A Non-Hermitian State-to-State Analysis of Transport in Aggregates with Multiple Endpoints
• Origin of Robust ${\mathbb{Z}}_2$ Topological Phases in Stacked Hermitian Systems: Non-Hermitian Level Repulsion
• Interplay of non-Hermitian skin effect and electronic correlations in the non-Hermitian Hubbard model via Real-space dynamical mean field theory
• Solution of Wave Acceleration and Non-Hermitian Jump in Nonreciprocal Lattices
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Hofstadter's Cocoon
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain
• Emergence of non-trivial phases in interacting non-Hermitian quasiperiodic chains with power-law hopping
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures
• Antiferromagnetism and spin excitations in a two-dimensional non-Hermitian Hatano-Nelson flux model
• Localization with non-Hermitian off-diagonal disorder
• Effects of kinked linear defects on planar flux line arrays
• Non-hermitean delocalization in an array of wells with variable-range widths
• Random weighted shifts
• Quantifying non-Hermiticity using single- and many-particle quantum properties
• Eigenvalues bifurcating from the continuum in two-dimensional potentials generating non-Hermitian gauge fields
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal