{
  "abstract": "Large-scale electronic-structure calculations require efficient access to local observables without explicitly constructing all occupied orbitals. We develop hierarchical Fourier phase projection (HPP), which organizes Fourier probes into a reusable spatial hierarchy that progressively removes short-range aliasing while exploiting density-matrix locality. The method provides systematic refinement from low-cost local estimates to the projection-exact limit of the chosen numerical occupation operator, without discarding previously evaluated responses. Tests using frozen Kohn--Sham Hamiltonians for semiconducting and metallic systems demonstrate controllable convergence of electron densities and nonlocal pseudopotential forces, weak size dependence of the probing resolution required for a fixed local accuracy, and near-linear growth of the direct computational cost at fixed probing workload. Inter-level changes further provide practical information for terminating the refinement at finite accuracy. HPP connects electronic locality, observable accuracy, and computational effort within a single hierarchical framework, providing a scalable route to local quantities in large-scale electronic-structure calculations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37814",
  "author_total": 5,
  "authors": [
    {
      "name": "Tao Hu"
    },
    {
      "name": "Weiqing Zhou"
    },
    {
      "name": "Zhichang Fu"
    },
    {
      "name": "Yechen Chen"
    },
    {
      "name": "Shengjun Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bw3e1ssqnt5er.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37814",
  "fulltext_url": null,
  "id": "bw3e1ssqnt5er",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37814",
  "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.mtrl-sci"
    ],
    [
      "openalex",
      "3107|Advanced Chemical Physics Studies"
    ]
  ],
  "openalex": "W7214909884",
  "pdf_url": "https://arxiv.org/pdf/2609.37814",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bw3e1ssqnt5er.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37814",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37814"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Hierarchical Fourier Phase Projection for Local Electronic Observables",
  "title_text": "Hierarchical Fourier Phase Projection for Local Electronic Observables",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:36Z",
  "url": "https://research.draconitic.com/paper/bw3e1ssqnt5er",
  "venue": "arXiv",
  "versions": []
}