Limitations of Green's function based topological invariants in correlated system

The topology of Green’s functions has recently attracted attention as a promising framework for identifying topological phases in correlated systems without explicit access to the many-body ground state. In this approach, both poles and zeros of the Green’s function can contribute to topological invariants. While poles correspond to physical quasiparticle excitations, the physical interpretation of Green’s function zeros remains ambiguous. In this work, we investigate the nature of these zeros using the Hubbard operator formalism and DMRG calculations. The two methods show good agreement in one-dimensional systems, supporting the Hubbard operator approach as a useful tool extendable to higher dimensions. Our results suggest that Green’s function–based invariants are not reliable indicators of the presence or absence of boundary states. Instead, they suggest that the emergence of edge modes at interfaces between distinct phases must be understood directly from the ground-state properties and their adiabatic connections.