Anomalous bulk-edge correspondence of nonlinear Rice-Mele model

TL;DR

This paper investigates the anomalous bulk-edge correspondence in a nonlinear Rice-Mele model, revealing new types of eigenvalues and a novel form of topological edge states induced by nonlinearity.

Contribution

It extends the understanding of bulk-edge correspondence to intrinsic nonlinear Hamiltonians, introducing the concept of anomalous BEC based on auxiliary nonlinear eigenvalues.

Findings

Identification of two types of nonlinear eigenvalues in the Rice-Mele model

Establishment of a novel anomalous bulk-edge correspondence

Demonstration of topological edge states arising from nonlinearity

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.