{
  "abstract": "We study the repulsive Hubbard model at half filling in the canonical ensemble and compare its thermodynamics with the spin-$\\frac12$ antiferromagnetic Heisenberg model at superexchange coupling $J_0(U)=4t^2/U$. For fixed hopping $t\\ne0$, bounded staggered fields $|h|\\le h_0$, and inverse temperatures $βJ_0(U)\\ge\\ell_0>0$, we establish a volume-uniform pressure comparison with error $O(U^{-3}+|h|U^{-2})$. On the Heisenberg field scale $h=J_0(U)x$, the error improves to $O(U^{-3})$ for bounded $x$. Using the quantum Lee--Yang theorem of Suzuki and Fisher, we obtain a volume-uniform $O(U^{-1})$ comparison of staggered magnetizations on compact positive intervals of the scaled field $x$. By combining a recent fermionic Lee--Yang theorem with analytic interpolation, we improve this estimate to $O(U^{-2}\\log U)$ in the thermodynamic limit. The latter analysis also establishes analyticity of the limiting Hubbard pressure at nonzero real fields. The improved comparison extends to vanishing positive fields satisfying $U^{-3}\\ll h(U)\\ll U^{-1}$, with error $O((1+\\log(U^3h(U)))/(U^3h(U)))$. Consequently, sufficiently low-temperature Heisenberg Néel order yields a quantitative positive lower bound on the Hubbard staggered magnetization in this regime. Furthermore, we prove $O(U^{-2})$ bounds on the double-occupancy and charge-defect densities and the normalized charge-density-wave second moment. At zero staggered field, this decay rate is optimal for both densities, even in the thermodynamic limit. Our approach uses finite-order Schrieffer--Wolff transformations and does not establish spontaneous Néel order at fixed finite $U$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.30663",
  "author_total": 1,
  "authors": [
    {
      "name": "Tadahiro Miyao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0r0wca3w12qjp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30663",
  "fulltext_url": null,
  "id": "0r0wca3w12qjp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30663",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7163042747",
  "pdf_url": "https://arxiv.org/pdf/2605.30663",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0r0wca3w12qjp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2605.30663",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30663"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Hubbard--Heisenberg Thermodynamic Comparison at Half Filling in a Fixed Staggered Field",
  "title_text": "Hubbard--Heisenberg Thermodynamic Comparison at Half Filling in a Fixed Staggered Field",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/0r0wca3w12qjp",
  "venue": "arXiv",
  "versions": []
}