Topological enhancement of non-normality in non-Hermitian skin effects

Abstract

The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.

arXiv comment36 pages, 15 figures

References in corpus (77)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Anderson Transitions
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• 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
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Non-Hermitian Chern bands
• Non-Hermitian Boundary Modes
• 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
• Non-Hermitian skin effect and chiral damping in open quantum systems
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Edge states and topological phases in non-Hermitian systems
• Non-Hermitian Topological Invariants in Real Space
• Critical non-Hermitian Skin Effect
• Observation of parity-time symmetry breaking in a single spin system
• Universal non-Hermitian skin effect in two and higher dimensions
• Non-Hermitian Topological Sensors
• Topologically protected defect states in open photonic systems with non-hermitian charge-conjugation and parity-time symmetry
• Non-Hermitian topological phenomena: A review
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Higher-order non-Hermitian skin effect
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• The strong side of weak topological insulators
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Non-Hermitean Random Matrix Theory: method of hermitization
• Tenfold Way for Quadratic Lindbladians
• Heralded magnetism in non-Hermitian atomic systems
• Second-order topological non-Hermitian skin effects
• Observation of critical phenomena in parity-time-symmetric quantum dynamics
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Non-Hermitian Kondo effect in ultracold alkaline-earth atoms
• Parity-time-symmetric topological superconductor
• Non-Hermitean Localization and De-Localization
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• Skin effect and winding number in disordered non-Hermitian systems
• Topological Phase Transition driven by Infinitesimal Instability: Majorana Fermions in Non-Hermitian Spintronics
• Hall Conductance of a Non-Hermitian Chern Insulator
• Mirror skin effect and its electric circuit simulation
• Statistical Topological Insulators
• Non-Hermitian Weyl Physics in Topological Insulator Ferromagnet Junctions
• Topological insulators beyond the Brillouin zone via Chern parity
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• Disorder-driven exceptional lines and Fermi ribbons in tilted nodal-line semimetals
• Non-Hermitian Skin Effects in Hermitian Correlated/Disordered Systems: Boundary-Sensitive/Insensitive Quantities and Pseudo Quantum Number
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator
• Equivalence of the effective non-hermitian Hamiltonians in the context of open quantum systems and strongly-correlated electron systems
• Effects of renormalization and non-Hermiticity on nonlinear responses in strongly-correlated electron systems
• Hermitian zero modes protected by nonnormality: Application of pseudospectra
• Exceptional band touching for strongly correlated systems in equilibrium
• Relation between exceptional points and the Kondo effect in $f$-electron materials
• Non-Hermitean De-Localization: Multiple Scattering and Bounds
• Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
• Topological invariant in three-dimensional band insulators with disorder
• Exceptional points in the one-dimensional Hubbard model
• A Non-Hermitean Particle in a Disordered World
• Majorana multipole response: General theory and application to wallpaper groups
• Skin Effect in Quadratic Lindbladian Systems: an Adjoint Fermion Approach
• Bulk-Edge Correspondence for Point-Gap Topological Phases in Junction Systems
• The Correlated Lloyd model: exact solution

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• Non-Hermitian Topology in Hermitian Topological Matter
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• Non-Markovian skin effect
• Transient amplification in stable Floquet media
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Dual Symmetry Classification of Non-Hermitian Systems and ${\mathbb{Z}}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
• Exceptional second-order topological insulators
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Non-Hermitian Hopf insulators
• Anderson Impurities In Edge States with Nonlinear and Dissipative Perturbations
• Scaling of pseudospectra in exponentially sensitive lattices
• Wiener-Hopf factorization and non-Hermitian topology for Amoeba formulation in one-dimensional multiband systems