Codimension-controlled universality of quantum Fisher information singularities at topological band-touching defects
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Quantum Physics arXiv:2604.01515 (quant-ph) [Submitted on 2 Apr 2026] Title:Codimension-controlled universality of quantum Fisher information singularities at topological band-touching defects Authors:C. A. S. Almeida View a PDF of the paper titled Codimension-controlled universality of quantum Fisher information singularities at topological band-touching defects, by C. A. S. Almeida View PDF HTML (experimental) Abstract:Topological phase transitions in generic multiband systems are mediated by band-touching defects whose codimension -- the number of momentum directions along which the gap closes linearly -- varies across universality classes. Although singular behavior of fidelity susceptibilities and quantum Fisher information (QFI) has been computed for specific models, no unifying principle connecting these results has been identified: it has remained unclear whether the controlling variable is spatial dimensionality, band structure, or an intrinsic geometric property of the defect. We resolve this question by showing that the singular contribution to the QFI with respect to the tuning parameter $m$ obeys a universal power-law scaling $\sim |m|^{p-2}$ for $p \neq 2$, with a logarithmic divergence $\sim \ln(1/|m|)$ at the marginal codimension $p = 2$, where $p$ denotes the codimension of the band-touching defect. This exponent is independent of spatial dimensionality, anisotropies, ultraviolet regularization, and additional gapped bands, and is protected by renormalization-group arguments at the linearized fixed point. The result unifies previously isolated observations for SSH chains ($p=1$), Chern insulators ($p=2$), and Weyl semimetals ($p=3$) as instances of a single codimension-dependent universality class, and reveals that only defects with $p \leq 2$ generate divergent information-geometric responses. This establishes a direct and previously missing link between topological classification in momentum space and quantum distinguishability in parameter space, with implications for metrological sensitivity near topological transitions and for the experimental detection of topological criticality via quantum geometric observables. Comments: Subjects: Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Cite as: arXiv:2604.01515 [quant-ph] (or arXiv:2604.01515v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.01515 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Carlos A. S. Almeida [view email] [v1] Thu, 2 Apr 2026 01:08:11 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled Codimension-controlled universality of quantum Fisher information singularities at topological band-touching defects, by C. A. S. AlmeidaView 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 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?)