Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems

Abstract

Recent foundational studies have established the bulk-edge correspondence for nonlinear eigenvalue problems using auxiliary eigenvalues $\hat{H}\Psi =\omega S(\omega )\Psi$, spanning both linear [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024)] and nonlinear [Chenxi Bai and Zhaoxin Liang, Phys. Rev. A. 111, 042201 (2025)] Hamiltionians. This progress prompts a fundamental question: Can eigenvalue nonlinearity generate observable physical phenomena absent in conventional approaches ($\hat{H}\Psi =E\Psi$)? In this work, we address this question by demonstrating the first uniquely nonlinear manifestation of the bulk-edge correspondence: fractional Thouless pumping of solitons. Through systematic investigation of nonlinear Thouless pumping in an extended Rice-Mele model incorporating next-nearest-neighbor (NNN) couplings, we uncover that NNN interaction parameters can induce fractional topological phases|even in the presence of quantized topological invariants as predicted by conventional linear approaches. Crucially, these fractional phases are naturally explained within the auxiliary eigenvalue framework, directly linking nonlinear spectral characteristics to the bulk-boundary correspondence. Our findings reveal novel emergent phenomena arising from the interplay between nonlinearity and NNN couplings, providing key insights for the design of topological insulators and the controlled manipulation of quantum edge states in nonlinear regimes.

arXiv comment13 pages, 8 figures

References in corpus (58)

• Berry Phase Effects on Electronic Properties
• Topological Photonics
• Topological Photonics
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Edge states and topological invariants of non-Hermitian systems
• Scheme to Achieve Silicon Topological Photonics
• Topological phases of non-Hermitian systems
• 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
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Probing topological invariants in the bulk of a non-Hermitian optical system
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Non-Hermitian bulk-boundary correspondence and auxiliary generalized Brillouin zone theory
• Non-Hermitian Topological Invariants in Real Space
• Topological defect launches 3D mound in the active nematic sheet of neural progenitors
• Critical non-Hermitian Skin Effect
• Topological phase transition in non-Hermitian quasicrystals
• Fermion Path Integrals And Topological Phases
• Observation of a dynamical topological phase transition
• New topological invariants in non-Hermitian systems
• Classification of topological phonons in linear mechanical metamaterials
• Active topological photonics
• Topological unification of time-reversal and particle-hole symmetries in non-Hermitian physics
• Thouless pumping and topology
• Phase-dependent chiral transport and effective non-Hermitian dynamics in a bosonic Kitaev-Majorana chain
• Quantized Nonlinear Thouless Pumping
• Manipulation of Dirac Cones in Mechanical Graphene
• Bloch Waves and Bloch Bands of Bose-Einstein Condensates in Optical Lattices
• Quantized Fractional Thouless Pumping of Solitons
• Nonlinear Thouless pumping: solitons and transport breakdown
• Quantisation and its breakdown in a Hubbard-Thouless pump
• Exotic Multifractal Conductance Fluctuations in Graphene
• Topological charge pumping in the interacting bosonic Rice-Mele model
• Nonlinear Polariton Fluids in a Flatband Reveal Discrete Gap Solitons
• Topological phase transition in coupled rock-paper-scissor cycles
• Effect of disorder on topological charge pumping in the Rice-Mele model
• Topological synchronization of coupled nonlinear oscillators
• The interacting Rice-Mele model: bulk and boundaries
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Interactions enable Thouless pumping in a nonsliding lattice
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Bulk-edge correspondence for nonlinear eigenvalue problems
• 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
• Breakdown of quantization in nonlinear Thouless pumping
• Weyl points of mechanical diamond
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Edge states of a diffusion equation in one dimension: Rapid heat conduction to the heat bath
• Chiral edge soliton in nonlinear Chern systems
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Nonlinearity-induced Fractional Thouless Pumping of Solitons
• Anomalous pumping in the non-Hermitian Rice-Mele model
• Nonlinear breathers with crystalline symmetries
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Chern numbers associated with the periodic Toda lattice

Cited by in corpus (2)

• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity