{
  "abstract": "Despite the exhaustive understanding gathered around non-interacting topological states of matter, there is no single method capable of systematically delivering simple, numerically efficient topological invariants that is applicable to all crystalline and non-crystalline systems alike. Here we revisit the spectral localizer operator, constructed from the Hamiltonian and position operators, and show how it can be treated it as an auxiliary zero-dimensional Hamiltonian whose topology encodes the higher dimensional phases of the parent Hamiltonian. Its classification reduces every topological invariant to a matrix signature or the sign of a Pfaffian for an appropriate localizer, both of which are simple to interpret and efficient to compute in real space. We validate this approach by deriving simple real-space invariants for weak and rotationally invariant crystalline phases that were previously beyond the grasp of the spectral localizer formalism, atomic limits that escape scattering invariants, phases that evade symmetry-based indicator methods, as well as phases that had no previously known invariant. Our work provides a systematic way to construct any non-interacting topological invariant for a crystalline or non-crystalline systems, opening avenues to classify and predict the topology of previously unexplored classes of materials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07775",
  "author_total": 3,
  "authors": [
    {
      "name": "Adam Yanis Chaou"
    },
    {
      "name": "Adolfo G. Grushin"
    },
    {
      "name": "Peru d'Ornellas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cnbnhxqn0rdv5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07775",
  "fulltext_url": null,
  "id": "cnbnhxqn0rdv5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07775",
  "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"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7212010880",
  "pdf_url": "https://arxiv.org/pdf/2609.07775",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cnbnhxqn0rdv5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07775",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07775"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Simple invariants for band topology",
  "title_text": "Simple invariants for band topology",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:48Z",
  "url": "https://research.draconitic.com/paper/cnbnhxqn0rdv5",
  "venue": "arXiv",
  "versions": []
}