Luttinger's Theorem Violation and Green's Function Topological Invariants in a Fractional Chern Insulator
Using exact diagonalization of the fermionic Harper-Hofstadter-Hubbard model, this study demonstrates the violation of Luttinger's theorem in fractional Chern insulators and elucidates how the fractional many-body Chern number and integer Green's function invariants are encoded in the Středa responses of the Luttinger integral and count, respectively, while proposing an experimental protocol to extract these topological invariants via local density-of-states measurements.