Cost scaling of MPS and TTNS simulations for 2D and 3D systems with area-law entanglement
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Quantum Physics arXiv:2601.08132 (quant-ph) [Submitted on 13 Jan 2026] Title:Cost scaling of MPS and TTNS simulations for 2D and 3D systems with area-law entanglement Authors:Thomas Barthel View a PDF of the paper titled Cost scaling of MPS and TTNS simulations for 2D and 3D systems with area-law entanglement, by Thomas Barthel View PDF HTML (experimental) Abstract:Tensor network states are an indispensable tool for the simulation of strongly correlated quantum many-body systems. In recent years, tree tensor network states (TTNS) have been successfully used for two-dimensional systems and to benchmark quantum simulation approaches for condensed matter, nuclear, and particle physics. In comparison to the more traditional approach based on matrix product states (MPS), the graph distance of physical degrees of freedom can be drastically reduced in TTNS. Surprisingly, it turns out that, for large systems in $D>1$ spatial dimensions, MPS simulations of low-energy states are nevertheless more efficient than TTNS simulations. With a focus on $D=2$ and 3, the scaling of computational costs for different boundary conditions is determined under the assumption that the system obeys an entanglement (log-)area law, implying that bond dimensions scale exponentially in the surface area of the associated subsystems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.08132 [quant-ph] (or arXiv:2601.08132v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.08132 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Thomas Barthel [view email] [v1] Tue, 13 Jan 2026 01:53:01 UTC (346 KB) Full-text links: Access Paper: View a PDF of the paper titled Cost scaling of MPS and TTNS simulations for 2D and 3D systems with area-law entanglement, by Thomas BarthelView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)