Topological states of matter were first introduced for noninteracting fermions on an infinite uniform lattice. Since then, substantial effort has been made to generalize these concepts to more complex settings. Recently, local markers have been developed that can describe the topological state of systems without translational symmetry and a well-defined gap. However, no local marker for interacting matter has been proposed yet that is capable of directly addressing an interacting system. Here, we suggest such a many-body local marker based on the single-particle Green's function. Using this marker we identify topological transitions in finite lattices of a Chern insulator with Anderson disorder and Hubbard interactions. Importantly, our proposal can be generalized to nonequilibrium systems.

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• Topological phases of matter
• Chern insulators
• Strongly correlated systems
• Exact diagonalization
• Hubbard model