{
  "abstract": "We study the structure of Gibbs states in weakly perturbed interacting fermionic systems. First, for a sparse Hamiltonian $H=H_0+V$ with a quadratic term $H_0$ and a non-quadratic perturbation $V$ of scale $ε$, we show that the Gibbs state $ρ_β$ decomposes into a convex combination of Gaussian states whenever the inverse temperature satisfies $β\\le O(\\log(1/ε))$. Moreover, we prove that this bound is asymptotically tight by establishing that $β\\le Θ(\\log(1/ε))$ is necessary for certain sparse Hamiltonians. This general framework applies directly to the weak-coupling (small-$\\vert{}U\\vert{}$) regime of the Fermi--Hubbard model with hopping $t$ and on-site interaction $U$ on any graph of maximum degree $D$. Complementarily, in the strong-coupling (small-$\\vert{}t\\vert{}$) regime, we show that the Gibbs state remains convex-Gaussian up to $β\\le O\\big(\\vert{}U\\vert{}^{-1}\\log(\\vert{}U\\vert{}/(D\\vert{}t\\vert{}))\\big)$, revealing a mechanism for convex-Gaussianity distinct from the weak-coupling setting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09608",
  "author_total": 2,
  "authors": [
    {
      "name": "Kaifeng Bu"
    },
    {
      "name": "Yuanjie Ren"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pmq7vsa6z7qx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09608",
  "fulltext_url": null,
  "id": "4pmq7vsa6z7qx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09608",
  "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.str-el"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7212128563",
  "pdf_url": "https://arxiv.org/pdf/2609.09608",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pmq7vsa6z7qx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09608",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09608"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Convex-Gaussianity of fermionic Gibbs states in perturbation theory",
  "title_text": "Convex-Gaussianity of fermionic Gibbs states in perturbation theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/4pmq7vsa6z7qx",
  "venue": "arXiv",
  "versions": []
}