[2608.14476] A Fixed Universal Determinant is Variationally Complete for Continuum Fermions Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Condensed Matter > Strongly Correlated Electrons arXiv:2608.14476 (cond-mat) [Submitted on 14 Aug 2026] Title: A Fixed Universal Determinant is Variationally Complete for Continuum Fermions Authors: Giuseppe Carleo , Riccardo Rossi View a PDF of the paper titled A Fixed Universal Determinant is Variationally Complete for Continuum Fermions, by Giuseppe Carleo and 1 other authors View PDF HTML (experimental) Abstract: How many Slater determinants does an accurate variational description of interacting fermions require? Exact expansions in a finite basis need combinatorially many, and state-of-the-art fermionic neural quantum states stack growing numbers of them. We prove that, in the norms that govern variational calculations, at most two are needed, independently of the number of particles and of the target accuracy. A single universal Slater determinant-specified in advance, independent of both the system and the state-multiplied by a smooth bosonic wave function approximates any fermionic wave function in up to three spatial dimensions in the first-order Sobolev norm, which controls the variational energy. Reaching the second-order Sobolev norm-for Coulomb interactions, the domain of the Hamiltonian, which bounds the variance of the local energy at the core of variational Monte Carlo-requires at most one additional fixed determinant, and only in three dimensions. Antisymmetry therefore costs at most two universal determinants and no expressiveness: generalized Slater-Jastrow neural quantum states are variationally complete. Comments: 4 pages, 2 figures Subjects: Strongly Correlated Electrons (cond-mat.str-el) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph) Cite as: arXiv:2608.14476 [cond-mat.str-el] (or arXiv:2608.14476v1 [cond-mat.str-el] for this version) https://doi.org/10.48550/arXiv.2608.14476 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Riccardo Rossi [ view email ] [v1] Fri, 14 Aug 2026 16:54:47 UTC (245 KB) Full-text links: Access Paper: View a PDF of the paper titled A Fixed Universal Determinant is Variationally Complete for Continuum Fermions, by Giuseppe Carleo and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cond-mat.str-el < prev | next > new | recent | 2026-08 Change to browse by: cond-mat math math-ph math.MP quant-ph References & Citations INSPIRE HEP 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