{
  "abstract": "{\\it Kramers-Wannier} duality of the quantum Ising chain is naturally realized as a noninvertible transformation on a finite periodic chain. Upon incorporating appropriate symmetry-twisted sectors, however, the duality can be promoted to an invertible unitary transformation. In this Letter, we classify when the Kramers-Wannier duality admits an invertible realization on a finite Hilbert space. We show that this is determined by the representation of the Ising bond algebra and establish a necessary and sufficient condition in terms of its two central elements. This representation-theoretic criterion unifies the conventional noninvertible realization with invertible constructions involving symmetry-twisted sectors and applies equally to other models with the same underlying bond algebra. As an explicit example, we find an order-disorder duality in a non-trivial realization of the Ising bond algebra that admits an invertible Kramers-Wannier duality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.20090",
  "author_total": 3,
  "authors": [
    {
      "name": "Akash Sinha"
    },
    {
      "name": "Pramod Padmanabhan"
    },
    {
      "name": "Vladimir Korepin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bacd9vv8y6t28.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.20090",
  "fulltext_url": null,
  "id": "bacd9vv8y6t28",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.20090",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213602084",
  "pdf_url": "https://arxiv.org/pdf/2609.20090",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bacd9vv8y6t28.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.20090",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.20090"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "When Is Kramers-Wannier Duality Invertible?",
  "title_text": "When Is Kramers-Wannier Duality Invertible?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/bacd9vv8y6t28",
  "venue": "arXiv",
  "versions": []
}