{
  "abstract": "Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39475",
  "author_total": 4,
  "authors": [
    {
      "name": "Simon Fell"
    },
    {
      "name": "Tobias F. Maier"
    },
    {
      "name": "Hans Peter Büchler"
    },
    {
      "name": "Nicolai Lang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/am5vaev6cf64p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39475",
  "fulltext_url": null,
  "id": "am5vaev6cf64p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39475",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7215035069",
  "pdf_url": "https://arxiv.org/pdf/2609.39475",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/am5vaev6cf64p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39475",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39475"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Excitation gap of a blockade structure with $\\mathbb{Z}_2$ topological order",
  "title_text": "Excitation gap of a blockade structure with ℤ_2 topological order",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/am5vaev6cf64p",
  "venue": "arXiv",
  "versions": []
}