{
  "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 $M_2^{\\rm NL}$, estimated by the SRE $M_2(\\tildeψ)$ of the computational-basis Schmidt representative $\\tildeψ$, 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, with an optimal constant. Combined with recent results, this yields the unconditional bracket $\\max\\{-\\log_2(1-4F),\\,M_2(\\tildeψ)-4\\}\\le M_2^{\\rm NL}\\le M_2(\\tildeψ)$. 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, the non-local magic, its estimate $M_2(\\tildeψ)$, 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 for two values of the fermion mass on lattices up to $8\\times 8$ ($\\sim 288$ qubits) with bond dimension up to $128$, we find that the non-local magic, as estimated by $M_2(\\tildeψ)$, 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28634",
  "author_total": 6,
  "authors": [
    {
      "name": "Raghav G. Jha"
    },
    {
      "name": "Jaber I. Taher"
    },
    {
      "name": "Muhammad Asaduzzaman"
    },
    {
      "name": "Goksu C. Toga"
    },
    {
      "name": "Bojko N. Bakalov"
    },
    {
      "name": "Alexander F. Kemper"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0b94cn92ggsww.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28634",
  "fulltext_url": null,
  "id": "0b94cn92ggsww",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28634",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-lat"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214360292",
  "pdf_url": "https://arxiv.org/pdf/2609.28634",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0b94cn92ggsww.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2609.28634",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28634"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-lat",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Non-stabilizerness and entanglement in $(2+1)$-dimensional SU(2) lattice gauge theory using tensor networks",
  "title_text": "Non-stabilizerness and entanglement in (2+1)-dimensional SU(2) lattice gauge theory using tensor networks",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/0b94cn92ggsww",
  "venue": "arXiv",
  "versions": []
}