Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks
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Quantum Physics arXiv:2512.11967 (quant-ph) [Submitted on 12 Dec 2025] Title:Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks Authors:Kaito Kobayashi, Benjamin Sappler, Frank Pollmann View a PDF of the paper titled Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks, by Kaito Kobayashi and 2 other authors View PDF HTML (experimental) Abstract:Isometric tensor network states (isoTNS) allow for efficient and accurate simulations of higher-dimensional quantum systems by enforcing an isometric structure. We bring this idea back to one dimension by introducing a holographic isoTNS ansatz: a (1+1)-dimensional lattice of isometric tensors where the horizontal axis encodes physical space and an auxiliary "holographic" axis boosts expressivity. Despite the enlarged geometry, contractions and local updates remain computationally efficient due to isometric constraints. We investigate this ansatz and benchmark it in comparison to matrix product states (MPS). First, we show that randomly initialized holographic isoTNS typically display volume-law entanglement even at modest bond dimension, surpassing the representational limits of MPS and related ansätze. Second, through analytic constructions and variational optimization, we demonstrate that holographic isoTNS can faithfully represent arbitrary fermionic Gaussian states, Clifford states, and certain short-time-evolved states under local evolution -- a family of states that is highly entangled but low in complexity. Third, to exploit this expressivity in broad situations, we implement a time-evolving block decimation (TEBD) algorithm on holographic isoTNS. While the method remains efficient and scalable, error accumulation over TEBD sweeps suppresses entanglement and leads to rapid deviations from exact dynamics. Overall, holographic isoTNS broaden the reach of tensor-network methods, opening new avenues to study physics in the volume-law regime. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2512.11967 [quant-ph] (or arXiv:2512.11967v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.11967 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Benjamin Sappler [view email] [v1] Fri, 12 Dec 2025 19:00:04 UTC (748 KB) Full-text links: Access Paper: View a PDF of the paper titled Holographic Representation of One-Dimensional Many-Body Quantum States via Isometric Tensor Networks, by Kaito Kobayashi and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cond-mat cond-mat.str-el 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?)