{
  "abstract": "Weak interactions at a two-dimensional quadratic band touching (QBT) can generate an exponentially small symmetry-breaking gap, $m\\sim e^{-A/V_1}$, that cannot be captured by every finite order of perturbation theory. We show that the singular quantum geometry of the gapped QBT converts this beyond-all-orders scale into an algebraically enhanced response. The quantum metric develops a momentum-space hot spot whose Brillouin-zone integral diverges logarithmically, and therefore grows algebraically when the gap is dynamically generated by interactions. Through the inverse-frequency Souza--Wilkens--Martin optical sum rule, the same amplification appears in the negative-first longitudinal optical moment, even though the ordinary optical conductivity remains $O(e^2/\\hbar)$ and its absorption threshold is exponentially small. We establish these results analytically for a massive QBT and verify them microscopically in an interacting kagome lattice model known to develop a spontaneous quantum anomalous Hall mass at its QBT from loop currents order. Our results identify quantum geometry as an asymptotic amplifier of nonperturbative interaction scales.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34607",
  "author_total": 4,
  "authors": [
    {
      "name": "Stefano Bilamour"
    },
    {
      "name": "René Meyer"
    },
    {
      "name": "Johanna Erdmenger"
    },
    {
      "name": "Domenico Di Sante"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1bgpbxhwbeh0s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34607",
  "fulltext_url": null,
  "id": "1bgpbxhwbeh0s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34607",
  "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.mtrl-sci"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7214704639",
  "pdf_url": "https://arxiv.org/pdf/2609.34607",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1bgpbxhwbeh0s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.34607",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34607"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.mtrl-sci",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Quantum-Geometric Amplification of Nonperturbative Interaction Scales",
  "title_text": "Quantum-Geometric Amplification of Nonperturbative Interaction Scales",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/1bgpbxhwbeh0s",
  "venue": "arXiv",
  "versions": []
}