  Recently, there is an interest in studying the bulk-edge correspondence for
nonlinear eigenvalues problems in a two-dimensional topological system with
spin-orbit coupling. By introducing auxiliary eigenvalues, 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 system 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
system.
