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.

6 pages, 4 figures

References in corpus (14)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Scheme to Achieve Silicon Topological Photonics
• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Topological Acoustics
• Analogs of quantum Hall effect edge states in photonic crystals
• Topological Origin of Non-Hermitian Skin Effects
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Active topological photonics
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals

Cited by in corpus (14)

• Resonant Excitation of Quasinormal Modes of Black Holes
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Protected chaos in a topological lattice
• Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect
• 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