Fragmented Topological Excitations in Generalized Hypergraph Product Codes
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Quantum Physics arXiv:2601.09850 (quant-ph) [Submitted on 14 Jan 2026] Title:Fragmented Topological Excitations in Generalized Hypergraph Product Codes Authors:Meng-Yuan Li, Yue Wu View a PDF of the paper titled Fragmented Topological Excitations in Generalized Hypergraph Product Codes, by Meng-Yuan Li and Yue Wu View PDF HTML (experimental) Abstract:Product code construction is a powerful tool for constructing quantum stabilizer codes, which serve as a promising paradigm for realizing fault-tolerant quantum computation. Furthermore, the natural mapping between stabilizer codes and the ground states of exactly solvable spin models also motivates the exploration of many-body orders in the stabilizer codes. In this work, we investigate the fracton topological orders in a family of codes obtained by a recently proposed general construction. More specifically, this code family can be regarded as a class of generalized hypergraph product (HGP) codes. We term the corresponding exactly solvable spin models \textit{orthoplex models}, based on the geometry of the stabilizers. In the 3D orthoplex model, we identify a series of intriguing properties within this model family, including non-monotonic ground state degeneracy (GSD) as a function of system size and non-Abelian lattice defects. Most remarkably, in 4D we discover \textit{fragmented topological excitations}: while such excitations manifest as discrete, isolated points in real space, their projections onto lower-dimensional subsystems form connected objects such as loops, revealing the intrinsic topological nature of these excitations. Therefore, fragmented excitations constitute an intriguing intermediate class between point-like and spatially extended topological excitations. In addition, these rich features establish the generalized HGP codes as a versatile and analytically tractable platform for studying the physics of fracton orders. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th) Cite as: arXiv:2601.09850 [quant-ph] (or arXiv:2601.09850v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.09850 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Meng-Yuan Li [view email] [v1] Wed, 14 Jan 2026 20:14:46 UTC (1,083 KB) Full-text links: Access Paper: View a PDF of the paper titled Fragmented Topological Excitations in Generalized Hypergraph Product Codes, by Meng-Yuan Li and Yue WuView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cond-mat cond-mat.str-el hep-th 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?)