Anomalous bulk-edge correspondence of the nonlinear Rice-Mele model

Bulk-edge correspondence 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 bulk-edge correspondence under the eigenvalue's nonlinearity in a linear Hamiltonian by introducing auxiliary eigenvalues [T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024)]. The purpose of this work aims to extend Isobe's analysis to uncover bulk-edge correspondence of the 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 form of bulk-edge correspondence based on these auxiliary nonlinear eigenvalues, which we term the anomalous bulk-edge correspondence of a nonlinear physical system. The concept of the anomalous bulk-edge correspondence defined herein provides an alternative perspective on the intricate interplay between topology and nonlinearity in the context of bulk-edge correspondence.