Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks

Quantum Physics arXiv:2609.28634 (quant-ph) [Submitted on 23 Sep 2026] Title:Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks Authors:Raghav G. Jha, Jaber I. Taher, Muhammad Asaduzzaman, Goksu C. Toga, Bojko N. Bakalov, Alexander F. Kemper View a PDF of the paper titled Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks, by Raghav G. Jha and 5 other authors View PDF HTML (experimental) Abstract:We study non-stabilizerness (magic) in the ground state of $(2+1)$-dimensional $\mathrm{SU}(2)$ Hamiltonian lattice gauge theory with matter, formulated in the dressed-site basis in the hardcore-gluon truncation and restricted to the zero baryon-number sector. Using matrix product states, we compute three facets of magic: the second-order stabilizer Rényi entropy (SRE) $M_2$, its non-local component $M_2^{\rm NL}$, and a lower bound in terms of the anti-flatness $F$ of the entanglement spectrum. We also prove a stronger form of the sandwich relation: $-\log_2(1-4F)\le M_2^{\rm NL}\le M_2$; the lower bound rests on a stronger inequality that we obtain for arbitrary Schmidt bases and rank, thus resolving the open problem of finding the maximal lower bound. We emphasize a structural distinction that makes the non-local quantities the physically preferred diagnostics: whereas the full SRE depends on the (non-unique) encoding of the gauge-invariant local Hilbert space into qubits, both the non-local magic and the anti-flatness are invariant under site-local re-encodings and are therefore intrinsic to the state and bipartition. By varying the gauge coupling on lattices up to $6\times 6$ with bond dimension up to $128$, we find that the non-local magic furnishes a sharper and more bond-dimension-friendly probe of the gauge-matter delocalization crossover compared to the full SRE or the gauge-invariant entanglement entropy, retaining a clear signal at bond dimensions well below those needed to converge the ground state itself. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat); High Energy Physics - Theory (hep-th) Cite as: arXiv:2609.28634 [quant-ph] (or arXiv:2609.28634v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.28634 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Raghav Govind Jha [view email] [v1] Wed, 23 Sep 2026 18:00:03 UTC (768 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks, by Raghav G. Jha and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: hep-lat 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?) 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?)