{
  "abstract": "$GW$+DMFT-type schemes replace the local part of a $GW$ self-energy by a separately computed local self-energy. A causal double counting removes a non-causal term from the hybridization (Lee and Haule, 2017), but the resulting total self-energy has been flagged as not guaranteed to be causal (Zhu and Chan, 2021). From the Herglotz representation, the spliced self-energy is causal if and only if its spectral measure is positive semi-definite. For translation-invariant single-band systems this becomes a momentum-resolved bound: the local weight may fall short of the local $GW$ weight by at most the momentum minimum of the $GW$ weight. On finite clusters, a mismatch between $GW$ and exact poles generically produces indefinite residues. On the Matsubara axis, a negative damping eigenvalue at one frequency certifies non-causality; passing does not establish causality. We examine these diagnostics in an idealized setting, not self-consistent $GW$+DMFT: one-shot $GW$ on the exact Green's function of small Hubbard clusters with the exact local self-energy inserted. At all 528 parameter sets, our computed $GW$ and exact self-energies pass both tests, as expected. The splice fails the pointwise test at 54 points, none at half filling, all at the lowest Matsubara frequency, and already at $U/t=0.5$; there the local $GW$ damping is 1.3-9 times the exact one. A block Pick test on eight frequencies, run with a second imaginary-time code, flags 481 of the 528 sets; for the other 47 it is inconclusive. Moment checks miss all of these, because the spliced high-frequency moment is exact. The Dyson Green's function is then non-causal too, yet passes the pointwise test everywhere tested. This version replaces a withdrawn one whose reported causality violations of $GW$ itself came from a sign error in the polarization; with the sign corrected, the computed $GW$ shows the expected positivity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00324",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael O. Atambo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/34x7hs14kse4q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00324",
  "fulltext_url": null,
  "id": "34x7hs14kse4q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.00324",
  "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.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7215969971",
  "pdf_url": "https://arxiv.org/pdf/2610.00324",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/34x7hs14kse4q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.00324",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00324"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mes-hall",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Splicing an exact local self-energy into $GW$: tests on small Hubbard clusters",
  "title_text": "Splicing an exact local self-energy into GW: tests on small Hubbard clusters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/34x7hs14kse4q",
  "venue": "arXiv",
  "versions": []
}