Many-Body Entanglement Properties of Finite Interacting Fermionic Hamiltonians
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Quantum Physics arXiv:2603.11300 (quant-ph) [Submitted on 11 Mar 2026] Title:Many-Body Entanglement Properties of Finite Interacting Fermionic Hamiltonians Authors:Irakli Giorgadze, Grayson Welch, Haixuan Huang, Elio J. König, Jukka I. Väyrynen View a PDF of the paper titled Many-Body Entanglement Properties of Finite Interacting Fermionic Hamiltonians, by Irakli Giorgadze and 4 other authors View PDF HTML (experimental) Abstract:We analyze many-body entanglement in interacting fermionic systems by using the $M$-body reduced density matrix. We demonstrate that if a particle number conserving fermionic Hamiltonian contains only up to $M$-body interaction terms, then its $N$-particle ground state cannot be maximally $M$-body entangled. As a key step in the proof, we show that the energy expectation value of a maximally $M$-body mixed state is equal to the spectral mean of the Hamiltonian on the corresponding $N$-particle subspace. We further demonstrate that the many-body entanglement structure of a ground state can place quantitative constraint on the interaction strength of its parent Hamiltonian. We illustrate the theorem and its implications in Hubbard and extended SYK models. Going beyond ground states, we analyze entanglement generation under unitary dynamics from Slater-determinant initial states in these models. We determine early-time growth and estimate entanglement saturation times. Finally, we derive explicit symmetry-refined saturation upper bounds for $M$-body entanglement in the presence of an Abelian symmetry. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.11300 [quant-ph] (or arXiv:2603.11300v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.11300 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Irakli Giorgadze [view email] [v1] Wed, 11 Mar 2026 20:55:08 UTC (5,755 KB) Full-text links: Access Paper: View a PDF of the paper titled Many-Body Entanglement Properties of Finite Interacting Fermionic Hamiltonians, by Irakli Giorgadze and 4 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)