Infinite magic and the emergence of the continuum

Quantum Physics arXiv:2610.20790 (quant-ph) [Submitted on 14 Oct 2026] Title:Infinite magic and the emergence of the continuum Authors:Leo Shaposhnik, Lorenzo Leone, Lennart Bittel, Dimitris Saraidaris, Alexander Jahn, Jens Eisert View a PDF of the paper titled Infinite magic and the emergence of the continuum, by Leo Shaposhnik and 5 other authors View PDF HTML (experimental) Abstract:Which features of a quantum state are needed for a relativistic quantum field theory to emerge from a lattice system? We address this question by establishing a quantitative relationship between the type classification of hyperfinite von Neumann algebras and the quantum-information-theoretic resource of nonstabilizerness, also called magic. Our results establish two complementary parts of this relationship. First, we prove that any stabilizer system on a lattice defines a canonical GNS Hilbert space in which local von Neumann algebras do not contain type III factors in their central decomposition. As an explicit example, we prove that for stabilizer systems with short-range order, the local algebras are isomorphic to tensor products of hyperfinite factors of type I or type II. This demonstrates that the absence of magic is accompanied by the absence of type III factors in the local algebras, therefore prohibiting the appearance of a quantum field theory. Second, for the hyperfinite factors of Araki, Woods and Powers, we prove a quantitative equivalence: The limiting factor is of type III if and only if the locally optimized min-relative entropy of magic diverges. This divergence is necessary to generate the continuous spectrum associated to a type III factor. Thus, in this setting, the emergence of a type III factor requires not merely the presence of magic, but an infinite amount of it. These results provide a rigorous setting supporting the proposal that infinite magic is a necessary structural ingredient for the emergence of a relativistic continuum from lattice systems. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:2610.20790 [quant-ph] (or arXiv:2610.20790v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2610.20790 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Leo Shaposhnik [view email] [v1] Wed, 14 Oct 2026 18:32:36 UTC (327 KB) Full-text links: Access Paper: View a PDF of the paper titled Infinite magic and the emergence of the continuum, by Leo Shaposhnik and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-10 Change to browse by: hep-th math math-ph math.MP 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?)