{
  "abstract": "Quantum anomalies are usually formulated in continuum field theory, where regularization may violate a classical symmetry. In a crystal, the compact Brillouin zone and the high-energy bands make that ultraviolet completion physical. This Perspective develops a unified lattice view of chiral and parity anomalies through the problem of realizing a single massless Dirac fermion. The central motif is a finite low-energy region in which the relevant symmetry is restored, embedded in a high-energy sector that breaks the symmetry and completes the lattice theory. In $1+1$ and $3+1$ dimensions, the quantized chiral response is protected by local chiral symmetry near the Fermi surface. In $2+1$ dimensions, the half-integer Hall response belongs to a single massless Dirac band with mirror symmetry, not to a generic massive Dirac insulator that breaks the symmetry explicitly. In both cases the lattice perspective reveals how the low-energy symmetry emerges from the high-energy sector and protects the anomalous and quantized response. Recent experimental progress in quantum materials is discussed in light of this unified view.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06349",
  "author_total": 1,
  "authors": [
    {
      "name": "Shun-Qing Shen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a65hvz6845det.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06349",
  "fulltext_url": null,
  "id": "a65hvz6845det",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06349",
  "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.other"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7212012434",
  "pdf_url": "https://arxiv.org/pdf/2609.06349",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a65hvz6845det.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06349",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06349"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.other",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Single Dirac Fermions on a Lattice: A Unified View of Chiral and Parity Anomalies in Condensed Matter",
  "title_text": "Single Dirac Fermions on a Lattice: A Unified View of Chiral and Parity Anomalies in Condensed Matter",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/a65hvz6845det",
  "venue": "arXiv",
  "versions": []
}