{
  "abstract": "Determining correlated ground states directly in the thermodynamic limit remains a central challenge in quantum many-body physics. Here we develop a quantum many-body bootstrap that yields a rigorous and tight lower bound on the thermodynamic ground-state energy of a fractional quantum Hall system together with an optimized reduced density matrix $ρ_W^\\star$ on a spatial window. For sufficiently tight bounds, we find that $ρ_W^\\star$ accurately reproduces the ground-state reduced density matrix, as directly tested by its fidelity with known model states. For exactly solvable Laughlin and Moore--Read parent Hamiltonians, the bootstrap also reproduces pair correlations and orbital entanglement spectra (OES). For Landau-level-projected Coulomb interactions across multiple fillings, the energy bounds closely track established thermodynamic estimates, while the window density matrix recovers the familiar $ν=1/3$ Laughlin and $ν=5/2$ Moore--Read states and the composite Fermi liquid at $ν=1/2$. More importantly, the same framework also resolves unsettled regimes. At $ν=1/4$, the OES and real-space correlations identify a composite Fermi liquid, while at $ν=12/5$ the combined diagnostics suggest $\\overline{\\mathrm{RR}}_3$ as the ground-state order. Our bootstrap therefore provides direct access to both ground-state energies and many-body structure in the thermodynamic limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21317",
  "author_total": 2,
  "authors": [
    {
      "name": "Qiang Gao"
    },
    {
      "name": "Taige Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r40t75jyzd11.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21317",
  "fulltext_url": null,
  "id": "2r40t75jyzd11",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21317",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7222604393",
  "pdf_url": "https://arxiv.org/pdf/2610.21317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2r40t75jyzd11.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2610.21317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21317"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Solving fractional quantum Hall problems with thermodynamic-limit bootstrap",
  "title_text": "Solving fractional quantum Hall problems with thermodynamic-limit bootstrap",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/2r40t75jyzd11",
  "venue": "arXiv",
  "versions": []
}