{
  "abstract": "We prove that weak long-range many-body interactions preserve the bulk gap of a free fermion system and that a quasi-local spectral flow transports the free ground state to ground states of the interacting system. Let $Φ_h$ be a free fermionic interaction, possibly including pairing terms, whose infinite-volume Majorana coefficient operator $h$ has no spectrum in $(-g,g)$, and let $\\mathcal V$ be an even self-adjoint many-body interaction. For sufficiently small $|λ|$, we construct pure ground states $ω_λ$ of the interacting bulk system $Φ_λ=Φ_h+λ\\mathcal V$ and quasi-local automorphisms $β_{0,λ}$ such that $ω_λ=ω_0\\circβ_{0,λ}$, where $ω_0$ is the free ground state of $Φ_h$. Each $ω_λ$ has a GNS Hamiltonian with gap at least $g-C_*|λ| \\|\\mathcal V\\|_*$, where $\\|\\cdot\\|_*$ is the relevant interaction norm. Our result allows polynomial decay of both the free coefficients and the many-body interaction. For two-site interactions on a uniformly discrete point set $Γ\\subset\\mathbb{R}^d$, a sufficient condition is decay as $(1+|x-y|)^{-\\varpi}$ with $\\varpi>2d$, for both the hopping and pairing coefficients and the interaction terms. The spectral-flow generator preserves the spatial exponent of the polynomial interaction norm, and its automorphisms satisfy locality bounds at that exponent. If $h$ and $\\mathcal V$ have stretched-exponential decay, so does the spectral-flow generator. The proof constructs the spectral flow and establishes the gap through an excitation-number comparison, using polynomial propagation bounds for evolved interactions proved in a companion paper.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40299",
  "author_total": 1,
  "authors": [
    {
      "name": "Stefan Teufel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qgnjz7wwmt4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40299",
  "fulltext_url": null,
  "id": "9qgnjz7wwmt4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40299",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.other"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qgnjz7wwmt4k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:28Z",
      "native_id": "2610.40299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.other",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Bulk gap stability and spectral flow for fermions with weak long-range interactions",
  "title_text": "Bulk gap stability and spectral flow for fermions with weak long-range interactions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9qgnjz7wwmt4k",
  "venue": "arXiv",
  "versions": []
}