{
  "abstract": "Luttinger theorem relates Fermi surface volume to electron density per spin $n$. It holds in an arbitrary Fermi liquid but is widely believed to break when a fermionic self-energy has a pole. We show that this is not necessarily the case. As an example, we consider a fermionic system consisting of two gapped bands, originating from a self-energy $Σ(ω, \\mathbf{k})$ with a pole, and a narrow residual quasiparticle band crossing $ω=0$, with a small residue $Z \\ll 1$ (a residual Fermi liquid). We consider Model I, in which $Z$ also renormalizes quasiparticle bandwidth $W$ to $ZW$ and Model II, in which $W$ remains unrenormalized. The Green's function for such a system $G(ω, \\mathbf{k})$ contains two zeros and three poles --- one from the quasiparticle band and two from the gapped bands. Yet, we show that in Model I, the Luttinger-Ward analysis is fully applicable for any $Z >0$, and the results are exactly the same as if the gapped bands did not exist. For Model II, the Luttinger-Ward analysis recovers once $Z$ exceeds some critical value, which depends on fermionic density.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04663",
  "author_total": 2,
  "authors": [
    {
      "name": "Artem Abanov"
    },
    {
      "name": "Andrey Chubukov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fccjy1mbrzsrq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04663",
  "fulltext_url": null,
  "id": "fccjy1mbrzsrq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04663",
  "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.str-el"
    ],
    [
      "openalex",
      "3104|Physics of Superconductivity and Magnetism"
    ]
  ],
  "openalex": "W7220724789",
  "pdf_url": "https://arxiv.org/pdf/2610.04663",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fccjy1mbrzsrq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04663",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04663"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Does a pole in the self-energy imply a violation of the Luttinger theorem?",
  "title_text": "Does a pole in the self-energy imply a violation of the Luttinger theorem?",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/fccjy1mbrzsrq",
  "venue": "arXiv",
  "versions": []
}