Bulk-edge correspondence for the nonlinear eigenvalues problem of the Haldane model

Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalue problems in a two-dimensional topological system with spin-orbit coupling. By employing the method of the auxiliary eigenvalues as introduced in T. Isobe et al., Phys. Rev. Lett. 132, 126601 (2024), the nonlinear bulk-edge correspondence was established. In this paper, taking the Haldane model as an example, we address that such a correspondence will appear in two-dimensional topological systems without spin-orbit coupling. The resulting edge states are characterized by the Chern number of the auxiliary energy band. A full phase diagram containing topological nontrivial phase, topological trivial phase, and metallic phase is obtained. Our work generalizes the study of the bulk-edge correspondence for nonlinear eigenvalue problems in two-dimensional systems.