{
  "abstract": "The two-dimensional metallic quantum critical problem is a long-standing puzzle that is widely believed to hold the key to resolving ubiquitous non-Fermi liquid behavior in strongly correlated electronic systems. In this study, we present a non-perturbative renormalization group (RG) analysis of the metallic Ising-nematic quantum critical point in two dimensions, formulated directly around an intrinsically nonlocal infrared (IR) boson propagator. Rather than treating the anomalous dynamical critical exponent $a$ as a fixed phenomenological parameter, we regard it as an intrinsic component of the fixed-point data to be determined from the internal consistency of the low-energy patch field theory under highly anisotropic scaling dimensions ($[k_0]=a+1$, $[k_x]=2$, $[k_y]=1$). While the leading two-loop diagrammatics vanish identically due to kinematic pole configurations, our three-loop evaluation reveals a profound structural asymmetry between the sectors: the fermion self-energy and Yukawa vertex receive non-vanishing logarithmic corrections, whereas the corresponding bosonic counter-term remains strictly zero. Consequently, we find that no self-consistent, intersecting fixed-point solution for the exponent $a$ exists within the three-loop truncation, failing to reproduce the physical value of $a \\approx 1.85$ observed in quantum Monte Carlo simulations. We conjecture that the cross-linked topology of the four-loop boson self-energy diagrams is exactly marginal and yields the minimal, mandatory bosonic counter-term required to restore multi-sector self-consistency. Our framework establishes a rigid multi-loop matching scheme necessary to uniquely pin down the critical exponent, and uncovers a stable phase space for field anomalous dimensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Phys. Rev. B 114, 245126 (2026)",
  "arxiv": "2605.30715",
  "author_total": 3,
  "authors": [
    {
      "name": "Hyeon Jung Kim"
    },
    {
      "name": "Kyoung-Min Kim"
    },
    {
      "name": "Ki-Seok Kim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9qcej24msakhz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.30715",
  "fulltext_url": null,
  "id": "9qcej24msakhz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.30715",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.30715",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9qcej24msakhz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2605.30715",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.30715"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Non-Perturbative Renormalization Group for Ising-Nematic Criticality: A Closed-Form Nonlocal Ansatz",
  "title_text": "Non-Perturbative Renormalization Group for Ising-Nematic Criticality: A Closed-Form Nonlocal Ansatz",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/9qcej24msakhz",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/zxpv-cqf9",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}