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.

36 pages, 15 figures

References in corpus (27)

• Anderson Transitions
• Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• 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
• Non-Hermitian topological phenomena: A review
• Higher-order non-Hermitian skin effect
• Non-Hermitian skin modes induced by on-site dissipations and chiral tunneling effect
• Non-Bloch band theory of non-Hermitian Hamiltonians in the symplectic class
• Second-order topological non-Hermitian skin effects
• Liouvillian Skin Effect: Slowing Down of Relaxation Processes without Gap Closing
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Skin effect and winding number in disordered non-Hermitian systems
• Unraveling the Non-Hermitian Skin Effect in Dissipative Systems
• 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
• 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
• Exceptional points in the one-dimensional Hubbard model
• 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

Cited by in corpus (17)

• Non-Hermitian Topology in Hermitian Topological Matter
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Field theory of non-Hermitian disordered systems
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• 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