Phase diagram of the nonlinear Dirac Hamiltonian, which demonstrates the nonlinear bulkboundary correspondence in the continuum model. The vertical axis represents the amplitude, and the horizontal axes correspond to the parameters of the nonlinear Dirac Hamiltonian. The blue curved surface shows the phase boundary that separates a trivial phase without boundary modes and a topological phase exhibiting localized modes at the left boundary. The red surfaces present the boundaries where the sign of the parameters of the Dirac Hamiltonian changes. The red lines show the phase boundaries at the surfaces of w = 1 and w = 2. In the linear limit ( w = 0), the topological phases are separated by the m = 0 axis, whereas the nonlinearity modifies the boundary of the topological phases.
