标题： 非线性Rice-Mele模型的异常体-边对应关系 显示英文标题

标题： Anomalous bulk-edge correspondence of nonlinear Rice-Mele model

摘要： 体-边对应关系（BEC）是拓扑物理领域的一个基本概念，阐明了表征体态的拓扑不变量与涌现的边界态之间的深刻相互作用。 这一研究方向的一个最新亮点是通过引入辅助本征值[\href{https://doi.org/10.1103/PhysRevLett.132.126601}{T. Isobe {\it 等，} 物理评论快报 132, 126601 (2024)}]，在线性哈密顿量中建立了本征值非线性下的BEC。 本工作的目的是将Isobe的分析扩展到内在非线性哈密顿量中，以揭示本征值非线性的BEC。 为了实现这一点，我们数值求解了非线性Rice-Mele（RM）模型，并识别出两种不同类型的非线性本征值：固有的非线性本征值以及通过引入辅助本征值而产生的本征值非线性。 此外，我们基于这些辅助非线性本征值建立了一种新的BEC形式，我们将其称为非线性物理系统的异常BEC。 本文定义的异常BEC概念为在BEC背景下拓扑学与非线性之间的复杂相互作用提供了新的视角。 显示英文摘要

摘要： 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.