Bulk-edge correspondence for nonlinear eigenvalue problems

Abstract

Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.

arXiv comment6 pages, 4 figures

References in corpus (68)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Topological Insulators in Three Dimensions
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Topological Photonics
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Weyl Semimetal in a Topological Insulator Multilayer
• Edge states and topological invariants of non-Hermitian systems
• Topological Insulator Materials
• Scheme to Achieve Silicon Topological Photonics
• Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Topological Acoustics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological Origin of Non-Hermitian Skin Effects
• Topological Band Theory for Non-Hermitian Hamiltonians
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Anomalous edge state in a non-Hermitian lattice
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum Hall effects in a Weyl Semi-Metal: possible application in pyrochlore Iridates
• Non-Hermitian Boundary Modes
• Spawning rings of exceptional points out of Dirac cones
• Weyl points and line nodes in gapless gyroid photonic crystals
• Topological defect launches 3D mound in the active nematic sheet of neural progenitors
• Classification of topological phonons in linear mechanical metamaterials
• Photonic Topological Insulating Phase Induced Solely by Gain and Loss
• Active topological photonics
• Non-Hermitian perspective of the band structure in heavy-fermion systems
• Exceptional rings in two-dimensional correlated systems with chiral symmetry
• Symmetry-protected nodal phases in non-Hermitian systems
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Topological Origin of Equatorial Waves
• Symmetry and Higher-Order Exceptional Points
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Exceptional Surfaces in PT-Symmetric Photonic Systems
• Symmetry-protected multifold exceptional points and their topological characterization
• Manipulation of Dirac Cones in Mechanical Graphene
• Mirror skin effect and its electric circuit simulation
• Exceptional rings protected by emergent symmetry for mechanical systems
• Magnetic susceptibility in three-dimensional nodal semimetals
• Exotic Multifractal Conductance Fluctuations in Graphene
• Nonlinear Polariton Fluids in a Flatband Reveal Discrete Gap Solitons
• Exceptional band touching for strongly correlated systems in equilibrium
• Topological phase transition in coupled rock-paper-scissor cycles
• Topological synchronization of coupled nonlinear oscillators
• Weyl semimetal phase in solid-solution narrow-gap semiconductors
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Circularly polarized topological edge states derived from optical Weyl points in semiconductor-based chiral woodpile photonic crystals
• Topological Toda lattice and nonlinear bulk-edge correspondence
• Weyl points of mechanical diamond
• Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
• Chiral edge soliton in nonlinear Chern systems
• Topological band theory of a generalized eigenvalue problem with Hermitian matrices: Symmetry-protected exceptional rings with emergent symmetry
• A symmetry-protected exceptional ring in a photonic crystal with negative index media
• Chern numbers associated with the periodic Toda lattice

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• Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Analytic bulk-edge connection in circular-symmetric models
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Frequency Domain Berry Curvature Effect on Time Refraction
• Chiral solitary waves in a nonlinear topological insulator model
• Nonlinearity-driven Topology via Spontaneous Symmetry Breaking
• Variational approach for the two-body problem in a multiband extended-Hubbard model
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping