{
  "abstract": "Weyl or Dirac fermions with the iconic linear energy-momentum relation and average density of states (ADOS) $ρ(E) \\sim |E|^{d-1}$ at energy $E$ in $d$ spatial dimensions, constitute a unique setup to study the disorder-driven semimetal-to-metal quantum phase transition (QPT) between ballistic (realized for weak disorder) and diffusive (stabilized at stronger disorder) quasiparticles. Such a QPT takes place only for $d>2$ and falls beyond the realm of the Anderson metal-to-insulator transition. From numerically computed ADOS (using the kernel polynomial method) in dirty Weyl systems in $d=2$ to $6$, here we show that $d=2$ and $d=4$ are the lower ($d_\\ell$) and upper ($d_u$) critical dimensions for such an unconventional QPT, respectively, as suggested from the solution of quasiparticle lifetime within the self-consistent Born approximation. Consequently, for $d \\geq 4$ the associated correlation length exponent is found to be $ν\\approx 0.5$ (within numerical accuracy). However, the dynamic scaling exponent at the quantum critical point is pinned close to $z \\approx d/2$ (numerically) for any $d \\geq 3$, which is shown to be an exact result from a field-theoretic renormalization group calculation. Therefore, Weyl semimetal-to-metal QPTs can be studied field theoretically around both $d_\\ell$ and $d_u$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30265",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongtai Li"
    },
    {
      "name": "Bitan Roy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ckdq0h3zdwwf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30265",
  "fulltext_url": null,
  "id": "5ckdq0h3zdwwf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30265",
  "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.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.mes-hall"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7214358154",
  "pdf_url": "https://arxiv.org/pdf/2609.30265",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ckdq0h3zdwwf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:11Z",
      "native_id": "2609.30265",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30265"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Upper critical dimension for dirty Weyl semimetal-to-metal quantum phase transitions",
  "title_text": "Upper critical dimension for dirty Weyl semimetal-to-metal quantum phase transitions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:11Z",
  "url": "https://research.draconitic.com/paper/5ckdq0h3zdwwf",
  "venue": "arXiv",
  "versions": []
}