{
  "abstract": "We introduce two-dimensional toric code models with additional long-range loop interactions. Our models preserve the topologically ordered ground states of the ordinary toric code, while confining anyons at zero temperature. For sufficiently long-ranged interactions, we argue that this confinement persists at finite temperatures, strongly constraining anyon mobility and giving rise to finite-temperature topological order. This topological phase acts as a self-correcting quantum memory and exhibits long-range entanglement. For shorter-ranged interactions, signatures of topological order survive only up to an exponentially large length scale at finite temperature, yielding a partially self-correcting quantum memory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37765",
  "author_total": 3,
  "authors": [
    {
      "name": "Jacopo Gliozzi"
    },
    {
      "name": "Taylor L. Hughes"
    },
    {
      "name": "Kyung-Su Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8089my74ks59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37765",
  "fulltext_url": null,
  "id": "a8089my74ks59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37765",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.37765",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8089my74ks59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.37765",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37765"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions",
  "title_text": "Long-Range Toric Code: Finite-Temperature Topological Order in Two Dimensions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/a8089my74ks59",
  "venue": "arXiv",
  "versions": []
}