{
  "abstract": "The entanglement spectra of fractional quantum Hall states contain universal fingerprints of their underlying topological order, as posited by the Li-Haldane conjecture. In this work, we uncover a finer universal structure within the entanglement spectra unravelled by projective measurements. Concretely, we study the projected ensemble of fractional quantum Hall states, defined as the collection of quantum states on a subsystem conditioned on measurement outcomes of its complement. We find that this ensemble exhibits a hidden hierarchy inside the Li-Haldane edge manifold: by conditioning on measurement outcomes, the entanglement spectrum's support is split into measurement-dependent sectors whose ranks we demonstrate are fixed by conformal field theory counting, an observation we dub the measurement-resolved Li-Haldane conjecture. For the non-Abelian Moore-Read state, this hierarchy is particularly rich: each parity-resolved edge manifold contains internal subspaces whose dimensions reproduce the conformal field theory counting of the opposite-parity sector. This structure persists even in realistic Coulomb-interacting ground states, establishing the projected ensemble as a sharp new probe of topological order beyond what the entanglement spectrum alone can detect.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03833",
  "author_total": 4,
  "authors": [
    {
      "name": "Daniel Spasic-Mlacak"
    },
    {
      "name": "Qi Camm Huang"
    },
    {
      "name": "Wen Wei Ho"
    },
    {
      "name": "Nigel R. Cooper"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3qswxmwvaph31.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03833",
  "fulltext_url": null,
  "id": "3qswxmwvaph31",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03833",
  "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.mes-hall"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7208708955",
  "pdf_url": "https://arxiv.org/pdf/2609.03833",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3qswxmwvaph31.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.03833",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03833"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Unravelling the Li-Haldane Conjecture with the Projected Ensemble",
  "title_text": "Unravelling the Li-Haldane Conjecture with the Projected Ensemble",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:07Z",
  "url": "https://research.draconitic.com/paper/3qswxmwvaph31",
  "venue": "arXiv",
  "versions": []
}