Latent symmetry in a minimal non-Hermitian trimer

Quantum Physics [Submitted on 16 Mar 2026] Latent symmetry in a minimal non-Hermitian trimer Paulo A. Brandão We study a minimal non-Hermitian trimer with latent symmetry formed by a cospectral pair of sites embedded in a three-site network with nonreciprocal couplings. We show that the model admits an exact decomposition into dark and bright sectors: the dark mode is spectrally isolated and retains a complex eigenvalue, while the bright sector reduces to an effective non-Hermitian dimer. For a suitable choice of parameters, this reduced subsystem becomes \mathcal{PT}-symmetric and exhibits partial spectral reality, with two real eigenvalues coexisting with the complex dark eigenvalue. At the critical point, the bright sector hosts an embedded second-order exceptional point, which renders the full trimer defective and gives rise to the characteristic Jordan-block dynamics. These results establish the non-Hermitian trimer as a minimal analytically solvable setting in which latent symmetry, sector-resolved \mathcal{PT} symmetry, and exceptional-point physics naturally coexist. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.15768 [quant-ph]   (or arXiv:2603.15768v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.15768 Focus to learn more Submission history From: Paulo Brandão [view email] [v1] Mon, 16 Mar 2026 18:01:21 UTC (192 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)