Abstract
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.
Data availability
The datasets generated during and/or analyzed during the current study are available from the corresponding author, Zhesen Yang, upon request.
Code availability
Code examples of key conclusions developed for this study and the software used are available in the GitHub repository at https://github.com/oaddao/CFD-code-examplesand have been archived in Zenodo with the https://doi.org/10.5281/zenodo.17404523. Other codes are available from the authors upon request.
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Acknowledgements
J. Huang and Z.Y. were sponsored by the National Key R&D Program of China (No. 2023YFA1407500), China Postdoctoral Science Foundation (No. 2025M773351) and the National Natural Science Foundation of China (No. 12322405, 12104450, 12047503). J. Hu was sponsored by the Ministry of Science and Technology (Grant No. 2022YFA1403901), National Natural Science Foundation of China (No. 12494594), and the New Cornerstone Investigator Program.
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Z. Yang conceived and supervised the research and acquired funding. J. Huang led the computational work, conducted the theoretical analysis and derivations, created the visualizations, and drafted the original manuscript. J. Hu contributed to the validation of the results through active discussion and data interpretation and acquired research funding. Both J. Hu and Z. Yang were involved in revising and editing the manuscript.
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Huang, J., Hu, J. & Yang, Z. Complex frequency detection in a subsystem. Commun Phys (2026). https://doi.org/10.1038/s42005-026-02524-8
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DOI: https://doi.org/10.1038/s42005-026-02524-8
