{
  "abstract": "We investigate topological phase transitions in a family of deformed $\\mathbb{Z}_3$ toric-code wavefunctions prepared from a cluster state by local deformations and projective measurements. Their norms map to the $Q=3$ Potts model for single-parameter deformations and to a three-state Ashkin–Teller-like (AT$_3$) construction with two independent four-spin couplings in the general case. Projected entangled-pair-state (PEPS) and variational uniform matrix-product-state (VUMPS) calculations identify the toric-code (TC) phase and phases in which electric ($e$) anyons are confined or condensed. These phases are separated by critical structures with central charges $c=4/5$, $8/5$, and isolated $c=1$ antiferromagnetic (AFM) endpoints. A normalized finite-distance $e$-anyon pair-state norm provides a Fredenhagen–Marcu-type check of the confinement boundary, while the topological data of the quantum double $D(\\mathbb{Z}_3)$ imply a topological entanglement entropy $\\gamma=\\log3$ throughout the gapped toric-code phase. Relative to the $\\mathbb{Z}_2$ case, the absence of sign-change folding leaves the AFM endpoints unfolded, and the extreme deformation reaches square ice with an emergent $U(1)$ one-form symmetry, Hilbert-space fragmentation, and exact scar configurations.",
  "abstract_shown": true,
  "affiliations": [
    "Korea University"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Yun-Tak Oh"
    },
    {
      "affs": [
        0
      ],
      "name": "Hyun-Yong Lee",
      "orcid": "0000-0003-4774-5213"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eskp6myh3m7a4.bib",
  "cited_by": 0,
  "doi": "10.21468/scipostphys.21.5.109",
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  "landing_url": "https://doi.org/10.21468/scipostphys.21.5.109",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "native_subjects": [
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  "pdf_url": "https://scipost.org/10.21468/SciPostPhys.21.5.109/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": "SciPost",
  "ris": "https://research.draconitic.com/paper/eskp6myh3m7a4.ris",
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  "subjects": [
    {
      "field": "physics",
      "origin": "feed-journal:physics/general",
      "subfield": "general"
    }
  ],
  "title": "Topological phase transition of deformed ${\\mathbb Z}_3$ toric code",
  "title_text": "Topological phase transition of deformed ℤ_3 toric code",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T12:20:12Z",
  "url": "https://research.draconitic.com/paper/eskp6myh3m7a4",
  "venue": "SciPost Physics",
  "versions": []
}