Complex frequency detection in a subsystem

Non-Hermitian physics, such as the non-Hermitian skin effect (NHSE), is well-established in classical platforms, but its emergence in intrinsically Hermitian or quantum systems remains a key challenge. Bridging this gap is crucial for connecting non-Hermitian concepts with foundational quantum many-body theory. Here, we systematically investigate this by studying a quantum subsystem with an effective non-Hermitian Hamiltonian arising from its exact frequency-dependent self-energy. We further employ complex-frequency detection, including excitation, synthesis, and fingerprint, to probe physical responses induced by complex driving frequencies. Our calculations reveal that both complex frequency excitation and synthesis are incompatible with the non-Hermitian approximation and cannot characterize the presence of the NHSE. In contrast, the complex-frequency fingerprint successfully detects the distinctive responses induced by the NHSE through the introduction of a double-frequency Green’s function. Our work provides a platform for studying non-Hermitian physics and its unconventional response in quantum systems rigorously without relying on any approximations. Non-Hermitian physics, like the non-Hermitian skin effect (NHSE), is well-explored in classical platforms but remains challenging in quantum systems. Here, the authors study a quantum subsystem described by an effective non-Hermitian Hamiltonian derived from its exact frequency-dependent self-energy, and show that only complex-frequency fingerprinting can uniquely detect NHSE-induced responses, providing a rigorous framework for exploring non-Hermitian phenomena without approximation.