{
  "abstract": "Decoherence-induced phase transitions (DIPTs) are associated with singular changes in a quantum system's entanglement structure as the decoherence strength varies. In many cases, their critical strengths depend monotonically on the Rényi index of the entanglement diagnostic, forming a Rényi hierarchy. We identify a general mechanism for this hierarchy based on correlation inequalities in replicated statistical models that describe these DIPTs. We demonstrate it in $\\mathbb{Z}_2$ topological stabilizer codes subject to independent phase-flip decoherence on each qubit and in a decohered rotor model with strong $\\text{U}(1)$ symmetry. When the relevant correlations diagnose the DIPTs, these inequalities imply that the critical decoherence strength is nondecreasing with integer Rényi index $R\\geq2$. We show that this mechanism also applies to a class of models with correlated decoherence.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30377",
  "author_total": 3,
  "authors": [
    {
      "name": "Zhou Yang"
    },
    {
      "name": "Yuri D. Lensky"
    },
    {
      "name": "Chao-Ming Jian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fawexyvzj3c67.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30377",
  "fulltext_url": null,
  "id": "fawexyvzj3c67",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30377",
  "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.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214684465",
  "pdf_url": "https://arxiv.org/pdf/2609.30377",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fawexyvzj3c67.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:52Z",
      "native_id": "2609.30377",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30377"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Mechanism for the Rényi Hierarchy of Decoherence-Induced Phase Transitions",
  "title_text": "A Mechanism for the Rényi Hierarchy of Decoherence-Induced Phase Transitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:52Z",
  "url": "https://research.draconitic.com/paper/fawexyvzj3c67",
  "venue": "arXiv",
  "versions": []
}