Spectral preservation under momentum-dependent similarity transformations in non-Hermitian lattice systems

[2608.14775] Spectral preservation under momentum-dependent similarity transformations in non-Hermitian lattice systems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Mesoscale and Nanoscale Physics arXiv:2608.14775 (cond-mat) [Submitted on 14 Aug 2026] Title: Spectral preservation under momentum-dependent similarity transformations in non-Hermitian lattice systems Authors: Ye Ma View a PDF of the paper titled Spectral preservation under momentum-dependent similarity transformations in non-Hermitian lattice systems, by Ye Ma View PDF HTML (experimental) Abstract: We investigate the conditions under which momentum-dependent similarity transformations preserve spectral properties of lattice Hamiltonians with open boundary conditions (OBC). While such transformations exactly preserve spectra in infinite systems, their application to finite systems introduces subtleties due to the long-range nature of the inverse transformation in real space. For general traceless $2\times 2$ Hamiltonians, we derive necessary and sufficient conditions for reduction to skew-diagonal form via constant similarity transforms, providing explicit transformation matrices for all cases. We then establish rigorous conditions for bulk spectral preservation under momentum-dependent transformations: the generalized Brillouin zone of $H$ must lie inside the smallest zero of $\det S(z)$ (the two-radius condition $r_{\mathrm{GBZ}}^{\max}<z_{\min}$), together with a spectral-stability (no critical non-Hermitian skin effect) condition on $H$. Two-sidedness of $S(z)$ governs only the modification of a finite number of boundary eigenvalues, not the bulk. Our results establish when bulk topological invariants computed in transformed coordinates reliably predict boundary physics, with implications for non-Hermitian systems, photonic crystals, and other platforms where chiral or hidden symmetries emerge only after appropriate basis changes. Subjects: Mesoscale and Nanoscale Physics (cond-mat.mes-hall) ; Other Condensed Matter (cond-mat.other) Cite as: arXiv:2608.14775 [cond-mat.mes-hall] (or arXiv:2608.14775v1 [cond-mat.mes-hall] for this version) https://doi.org/10.48550/arXiv.2608.14775 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ye Ma [ view email ] [v1] Fri, 14 Aug 2026 16:25:27 UTC (3,720 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral preservation under momentum-dependent similarity transformations in non-Hermitian lattice systems, by Ye Ma View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.mes-hall < prev | next > new | recent | 2026-08 Change to browse by: cond-mat cond-mat.other References & Citations NASA ADS Google 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? ) 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? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) 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? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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