{
  "abstract": "We construct and study lattice realizations of finite 2-group symmetries in ${2+1}$d quantum lattice systems with finite-dimensional tensor-product Hilbert spaces. We focus on two broad classes of 2-groups with 0-form symmetry group $G$ and 1-form symmetry group $A$: split 2-groups with trivial Postnikov class ${[β]\\in\\mathcal{H}^3(G,A)}$, and central 2-groups with trivial action ${ρ\\colon G\\to\\text{Aut}(A)}$. In both cases, we construct symmetry operators on the full tensor-product Hilbert space that become 2-group symmetry operators when restricted to the topological subspace of the lattice $A$ 1-form symmetry. While the lattice split 2-group symmetry operators are onsite, the lattice central 2-group symmetry operators are not, and can only be made onsite after introducing ancillae. We extensively explore various manifestations of $ρ$ and $[β]$ for these lattice 2-group symmetry operators and demonstrate their agreement with expectations from quantum field theory. These manifestations arise in the transformation of operators carrying symmetry charge, the structure of lattice 2-group symmetry defects, and the dual fusion 2-category symmetries obtained by gauging the lattice 2-group symmetries. We further propose families of local symmetric Hamiltonians for both classes of lattice 2-group symmetries and identify exactly solvable limits lying in phases with spontaneous 2-group symmetry breaking and nontrivial symmetry-enriched topological order. In one such limit, the gauged Hamiltonians are exactly solvable lattice realizations of the corresponding 2-group gauge theories, whose ground-state degeneracies we calculate.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10682",
  "author_total": 2,
  "authors": [
    {
      "name": "Lucas Z. Brito"
    },
    {
      "name": "Salvatore D. Pace"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5az761r1mgw4s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10682",
  "fulltext_url": null,
  "id": "5az761r1mgw4s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10682",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212266114",
  "pdf_url": "https://arxiv.org/pdf/2609.10682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5az761r1mgw4s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.10682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10682"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Lattice 2-group symmetries: operators, defects, and gauging",
  "title_text": "Lattice 2-group symmetries: operators, defects, and gauging",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/5az761r1mgw4s",
  "venue": "arXiv",
  "versions": []
}