{
  "abstract": "Haar randomness is the standard null model for quantum typicality, scrambling, and random-matrix formulations of thermalization. In many physical settings, however, randomness is naturally constrained to subspaces of Hilbert space. This structure arises, in particular, both in systems with symmetry-resolved sectors and in the Eigenstate Thermalization Hypothesis (ETH), where mesoscopic energy windows define subspaces in which nearby energy eigenstates are mixed. Motivated by these settings, we consider a Block-Unitary Ensemble consisting of independently Haar-random unitaries acting on each subspace. We develop a constructive Weingarten Calculus for this ensemble, providing a unified framework across quantum information and many-body physics. This construction reveals a symmetry-resolved Schur-Weyl duality, where the relevant commutant is not the ordinary permutation algebra, but the one of color-preserving permutations. We apply this framework to quantum states under symmetry constraints and to energy-resolved ensembles for ETH.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30385",
  "author_total": 2,
  "authors": [
    {
      "name": "Daniele Iannotti"
    },
    {
      "name": "Elisa Vallini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/75gfmzpq26tn2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30385",
  "fulltext_url": null,
  "id": "75gfmzpq26tn2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30385",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7214573171",
  "pdf_url": "https://arxiv.org/pdf/2609.30385",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/75gfmzpq26tn2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2609.30385",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30385"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Colored Weingarten Calculus for Block-Unitary Ensemble",
  "title_text": "Colored Weingarten Calculus for Block-Unitary Ensemble",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/75gfmzpq26tn2",
  "venue": "arXiv",
  "versions": []
}