Information in Many-body Eigenstates: A Question of Learnability
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Quantum Physics arXiv:2605.03043 (quant-ph) [Submitted on 4 May 2026] Title:Information in Many-body Eigenstates: A Question of Learnability Authors:Maksymilian Kliczkowski, Jarosław Pawłowski, Masudul Haque View a PDF of the paper titled Information in Many-body Eigenstates: A Question of Learnability, by Maksymilian Kliczkowski and 2 other authors View PDF HTML (experimental) Abstract:To what extent do individual eigenstates encode information of their underlying Hamiltonian, and how does this depend on their spectral position? For many-body quantum systems, this issue is widely understood in terms of the differing nature of the eigenstates near the spectral edges (low-entanglement, highly-structured eigenstates) and those far from the spectral edges (high-entanglement, near-random eigenstates). Utilizing the availability of machine learning tools, we introduce a new way to quantify the information contained in eigenstates: for a particular learning architecture, how precisely can the Hamiltonian be reconstructed from a single eigenstate? We refer to this property as learnability; it serves as a new, alternative measure of the information content of eigenstates, made possible by machine learning. Using an encoder-decoder neural network and a physics-inspired loss function, we demonstrate how the distinction between two types of eigenstates is manifested as a difference in learnability. For spectral-edge eigenstates, the prediction accuracy is much better, and fewer eigenstates are required to learn the Hamiltonian, compared to mid-spectrum eigenstates. Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn) Cite as: arXiv:2605.03043 [quant-ph] (or arXiv:2605.03043v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.03043 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Maksymilian Kliczkowski [view email] [v1] Mon, 4 May 2026 18:11:29 UTC (4,174 KB) Full-text links: Access Paper: View a PDF of the paper titled Information in Many-body Eigenstates: A Question of Learnability, by Maksymilian Kliczkowski and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cond-mat cond-mat.dis-nn 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?)