{
  "abstract": "The conventional Bloch quantum geometric tensor (QGT) describes electric-dipole geometry for spatially uniform perturbations and vertical Bloch transitions. We develop a broader framework linking quantum geometry to local and nonlocal electromagnetic response in gauge-field space, placing this tensor within a hierarchy of electric and magnetic multipole quantum geometries. The intrinsic antisymmetric adiabatic response in every electromagnetic channel is a Berry curvature in the space of its conjugate fields. The field-dependent projector uniquely fixes the QGT for that channel, pairing the response curvature with a quantum metric. This construction extends to spatially nonuniform perturbations, whose finite momentum transfer induces nonvertical Bloch transitions. We explicitly construct the current--current QGT connecting Bloch states at $\\mathbf{k}\\pm\\mathbf{q}/2$, providing a unified metric and curvature description of nonlocal current response. In the doubled Brillouin zone, tangential derivatives generate conventional momentum-space QGT multipoles, whereas normal derivatives connect finite-momentum geometry to uniform electric- and magnetic-multipole-pair QGTs. We derive this connection through second order in $\\mathbf{q}$. The finite-momentum curvature governs the intrinsic nonlocal Hall response, while an inverse-frequency moment of symmetric optical absorption probes the index-symmetric metric sector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41610",
  "author_total": 4,
  "authors": [
    {
      "name": "Bin Wang"
    },
    {
      "name": "Fuming Xu"
    },
    {
      "name": "Lei Zhang"
    },
    {
      "name": "Jian Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/abfrr0r8fkv5q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41610",
  "fulltext_url": null,
  "id": "abfrr0r8fkv5q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41610",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41610",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/abfrr0r8fkv5q.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41610",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41610"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Hierarchy of Electromagnetic Gauge Field Quantum Geometries",
  "title_text": "Hierarchy of Electromagnetic Gauge Field Quantum Geometries",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/abfrr0r8fkv5q",
  "venue": "arXiv",
  "versions": []
}