Anomalous bulk-edge correspondence of nonlinear Rice-Mele model

Abstract

Bulk-edge correspondence (BEC) constitutes a fundamental concept within the domain of topological physics, elucidating the profound interplay between the topological invariants that characterize the bulk states and the emergent edge states. A recent highlight along this research line consists of establishing BEC under the eigenvalue's nonlinearity in a linear Hamiltonian by introducing auxiliary eigenvalues [\href{https://doi.org/10.1103/PhysRevLett.132.126601}{ T. Isobe {\it et al.,} Phys. Rev. Lett. 132, 126601 (2024)}]. The purpose of this work aims to extend Isobe's analysis to uncover BEC of eigenvalue's nonlinearity in intrinsic nonlinear Hamiltonians. To achieve this, we numerically solve the nonlinear Rice-Mele (RM) model and identify two distinct types of nonlinear eigenvalues: the intrinsically nonlinear eigenvalues and the eigenvalue's nonlinearity introduced through the incorporation of auxiliary eigenvalues. Furthermore, we establish a novel form of BEC based on these auxiliary nonlinear eigenvalues, which we term the anomalous BEC of a nonlinear physical system. The concept of the anomalous BEC defined herein provides a novel perspective on the intricate interplay between topology and nonlinearity in the context of BEC.

9 pages, 4 figures

References in corpus (26)

• Quantum Spin Hall Effect and Topological Phase Transition 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
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Active topological photonics
• Chiral symmetry and bulk--boundary correspondence in periodically driven one-dimensional systems
• Thouless pumping and topology
• Quantized Nonlinear Thouless Pumping
• Quantized Fractional Thouless Pumping of Solitons
• Quantisation and its breakdown in a Hubbard-Thouless pump
• Realization of Fractional Chern Insulators in the Thin-Torus-Limit with Ultracold Bosons
• Quantum Transport of Bosonic Cold Atoms in Double Well Optical Lattices
• Quantized pumping and phase diagram topology of interacting bosons
• Fractional charge pumping of interacting bosons in one-dimensional superlattice
• Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model
• Interactions enable Thouless pumping in a nonsliding lattice
• Bulk-edge correspondence for nonlinear eigenvalue problems
• Topological boundary invariants for Floquet systems and quantum walks
• Breakdown of quantization in nonlinear Thouless pumping
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps

Cited by in corpus (5)

• Fractional Thouless pumping of solitons: a unique manifestation of bulk-edge correspondence of nonlinear eigenvalue problems
• Topological Phases in Non-Hermitian Nonlinear-Eigenvalue Systems
• Frequency Domain Berry Curvature Effect on Time Refraction
• Nonreciprocity Induced Fractional Nonlinear Thouless Pumping
• Soliton Pumping in the Rice-Mele Model with On-Cell Kerr Nonlinearity