Invisible flat bands on a topological chiral edge

We prove that invisible bands associated with zeros of the single-particle Green's function exist ubiquitously at topological interfaces of two-dimensional Chern insulators, dual to the chiral edge/domain-wall modes. We verify this statement in a repulsive Hubbard model with a topological flat band, using real-space dynamical mean-field theory to study the domain walls of its ferromagnetic ground state. Moreover, our numerical results show that the chiral modes are split into branches due to the interaction and that the branches are connected by invisible flat bands. Our work provides deeper insight into interacting topological systems.