Complex Frequency Fingerprint: Interacting Driven Non-Hermitian Skin Effect

The excitation properties of quantum many-body systems are encoded in their response functions. These functions define an associated response Hamiltonian, which is intrinsically non-Hermitian due to the dissipative nature of retarded responses, even in closed systems. By analyzing its eigenvalues and eigenstates, one obtains a unique characterization of the system, referred to as the complex frequency fingerprint. Using this framework, we demonstrate that interactions alone can give rise to both point-gap topology and the non-Hermitian skin effect. Unlike the dissipation-induced skin effect, this interaction-driven phenomenon exhibits pronounced frequency dependence. We further introduce a complex-frequency density of states framework that distinctly separates non-Hermitian skin modes from topological edge modes.