Latent symmetry in a minimal non-Hermitian trimer
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Quantum Physics arXiv:2603.15768 (quant-ph) [Submitted on 16 Mar 2026] Title:Latent symmetry in a minimal non-Hermitian trimer Authors:Paulo A. Brandão View a PDF of the paper titled Latent symmetry in a minimal non-Hermitian trimer, by Paulo A. Brand\~ao View PDF HTML (experimental) Abstract: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 arXiv-issued DOI via DataCite (pending registration) Submission history From: Paulo Brandão [view email] [v1] Mon, 16 Mar 2026 18:01:21 UTC (192 KB) Full-text links: Access Paper: View a PDF of the paper titled Latent symmetry in a minimal non-Hermitian trimer, by Paulo A. Brand\~aoView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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 Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)