Anomalous bulk-edge correspondence of nonlinear Rice-Mele model

• URL: http://arxiv.org/abs/2501.02478v1
• Date: Sun, 05 Jan 2025 08:30:37 GMT
• Title: Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
• Authors: Chenxi Bai, Zhaoxin Liang,
• Abstract summary: This work aims to extend Isobe's analysis to uncover BEC of eigenvalue's nonlinearity in intrinsic nonlinear Hamiltonians. We numerically solve the nonlinear Rice-Mele (RM) model and identify two distinct types of nonlinear eigenvalues. We establish a novel form of BEC based on these auxiliary nonlinear eigenvalues, which we term the anomalous BEC of a nonlinear physical system.
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• 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.

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