Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions
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Quantum Physics arXiv:2512.12010 (quant-ph) [Submitted on 12 Dec 2025] Title:Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions Authors:Hongrui Chen, Cambyse Rouzé, Jielun Chen, Jiaqing Jiang, Samuel O. Scalet, Yongtao Zhan, Garnet Kin-Lic Chan, Lexing Ying, Yu Tong View a PDF of the paper titled Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions, by Hongrui Chen and 8 other authors View PDF HTML (experimental) Abstract:We propose a randomized algorithm to compute the log-partition function of weakly interacting fermions with polynomial runtime in both the system size and precision. Although weakly interacting fermionic systems are considered tractable for many computational methods such as the diagrammatic quantum Monte Carlo, a mathematically rigorous proof of polynomial runtime has been lacking. In this work we first extend the proof techniques developed in previous works for proving the convergence of the cumulant expansion in periodic systems to the non-periodic case. A key equation used to analyze the sum of connected Feynman diagrams, which we call the tree-determinant expansion, reveals an underlying tree structure in the summation. This enables us to design a new randomized algorithm to compute the log-partition function through importance sampling augmented by belief propagation. This approach differs from the traditional method based on Markov chain Monte Carlo, whose efficiency is hard to guarantee, and enables us to obtain a algorithm with provable polynomial runtime. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Numerical Analysis (math.NA); Computational Physics (physics.comp-ph) Cite as: arXiv:2512.12010 [quant-ph] (or arXiv:2512.12010v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.12010 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Yu Tong [view email] [v1] Fri, 12 Dec 2025 20:00:39 UTC (61 KB) Full-text links: Access Paper: View a PDF of the paper titled Convergence of the Cumulant Expansion and Polynomial-Time Algorithm for Weakly Interacting Fermions, by Hongrui Chen and 8 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.NA math math-ph math.MP math.NA physics physics.comp-ph 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)