{
  "abstract": "Planar parity-preserving tensor networks (ppTNs) admit a fermionic formulation in which the Gaussian, efficiently contractible limit is deformed by local interactions. We investigate how many-body methods can be used to analyze such contractions in a minimal two-parameter ppTN. Its contraction is simultaneously an interacting fermionic partition function, a loop gas, a deformed toric-code norm, and a quartic Ising model, allowing the same phase diagram to be approached with complementary tools. At its center lies a `topological island', characterized beyond the Gaussian limit by a boundary-twist $\\mathbb Z_2$ indicator that reduces to Chern-number parity and admits a loop-winding interpretation under duality. Fermionic perturbation theory predicts the interacting phase boundaries, tensor-network numerics establish their critical behavior, and the loop and spin descriptions reveal a self-dual line with a $c=1$ four-state-Potts multicritical fixed point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40004",
  "author_total": 5,
  "authors": [
    {
      "name": "Maksimilian Usoltcev"
    },
    {
      "name": "Nguyen Hanh Dung"
    },
    {
      "name": "Carolin Wille"
    },
    {
      "name": "Matteo Rizzi"
    },
    {
      "name": "Alexander Altland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eywk74v0yjpc2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40004",
  "fulltext_url": null,
  "id": "eywk74v0yjpc2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40004",
  "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",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7215098357",
  "pdf_url": "https://arxiv.org/pdf/2609.40004",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eywk74v0yjpc2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.40004",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40004"
    }
  ],
  "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": "Many-body topology in parity-preserving tensor networks",
  "title_text": "Many-body topology in parity-preserving tensor networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/eywk74v0yjpc2",
  "venue": "arXiv",
  "versions": []
}