{
  "abstract": "We present an efficient mixed deterministic-stochastic approach for constructing the Coulomb operator in real space that preserves accuracy across the full spectral range. The dominant long-range components of the interaction are captured deterministically via a compact, low-rank approximation, constructed using Chebyshev-filtered subspace iteration, while the remaining spectral tail is treated using unbiased probing with a small number of stochastic vectors. The resulting operator is benchmarked within self-consistent field calculations for the extended Hubbard Hamiltonian on periodic, perturbed, and non-periodic three-dimensional lattices. We account for stochastic bias in observables by implementing a jackknife correction. The method systematically improves with deterministic rank and stochastic sample count, while substantially reducing the computational cost of constructing the Coulomb matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10189",
  "author_total": 5,
  "authors": [
    {
      "name": "Nafiz Faiaz"
    },
    {
      "name": "Tucker Allen"
    },
    {
      "name": "Dimitri Bazile"
    },
    {
      "name": "Kajsa Williams"
    },
    {
      "name": "Daniel Neuhauser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3skw767wvh19m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10189",
  "fulltext_url": null,
  "id": "3skw767wvh19m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10189",
  "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",
      "physics.chem-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.10189",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3skw767wvh19m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.10189",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10189"
    }
  ],
  "subjects": [
    {
      "field": "chemistry",
      "origin": "arxiv:physics.chem-ph",
      "subfield": "physical"
    }
  ],
  "title": "Efficient Deterministic-Stochastic Representation of the Coulomb Operator in Real Space",
  "title_text": "Efficient Deterministic-Stochastic Representation of the Coulomb Operator in Real Space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:12Z",
  "url": "https://research.draconitic.com/paper/3skw767wvh19m",
  "venue": "arXiv",
  "versions": []
}