Dual Quantum Geometric Tensors and Local Topological Invariant
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Quantum Physics arXiv:2604.09725 (quant-ph) [Submitted on 9 Apr 2026] Title:Dual Quantum Geometric Tensors and Local Topological Invariant Authors:Rongjie Cui, Longjun Xiang, Fuming Xu, Jian Wang View a PDF of the paper titled Dual Quantum Geometric Tensors and Local Topological Invariant, by Rongjie Cui and 3 other authors View PDF HTML (experimental) Abstract:The conventional quantum geometric tensor (QGT) is Hermitian, with a real symmetric quantum metric and an imaginary antisymmetric Berry curvature. We show that the Zeeman QGT is generically non-Hermitian and admits a natural decomposition into normal and anomalous metric-curvature sectors. The normal sector reduces to the conventional Hermitian structure, whereas the anomalous sector contains an imaginary symmetric metric-like tensor and a real antisymmetric curvature-like tensor with no counterpart in the standard QGT. In a two-dimensional Dirac system, the anomalous Zeeman curvature develops a radial flux singularity that is Hodge-dual to the tangential winding field of the Dirac node. This recasts the same local $\pi_1$ topology into a curvature-flux language, analogous to the flux representation of global $\pi_2$ topology by the conventional Berry curvature. At the level of linear response, the four symmetry-resolved components of the gyrotropic conductivity are in one-to-one correspondence with the four components of the Zeeman QGT, while their distinct low-frequency scalings provide an additional diagnostic for isolating the underlying geometric sector. The reciprocal kinetic magnetoelectric response offers a complementary experimental route to probe the same structure. These results establish a unified framework connecting non-Hermitian Zeeman quantum geometry, local Dirac-node topology, and measurable transport signatures. Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Materials Science (cond-mat.mtrl-sci) Cite as: arXiv:2604.09725 [quant-ph] (or arXiv:2604.09725v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.09725 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Longjun Xiang [view email] [v1] Thu, 9 Apr 2026 08:00:50 UTC (139 KB) Full-text links: Access Paper: View a PDF of the paper titled Dual Quantum Geometric Tensors and Local Topological Invariant, by Rongjie Cui and 3 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cond-mat cond-mat.mes-hall cond-mat.mtrl-sci 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?) 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?)