{
  "abstract": "Although Hamiltonians govern wave-matter interactions, conventional characterizations of topological phases of matter require more than the Hamiltonian alone, relying on global invariants defined on closed reciprocal-space manifolds or local commutation relations with position operators. This spatial dependence precludes a unique characterization of topological phases on an abstract platform, whose Hamiltonian can be defined independently of its spatial embedding. Here we establish a framework for characterizing universal topological phases, grounded in the invariance of topological features under arbitrary Hamiltonian-preserving deformations. We construct a Hamiltonian-based spatial embedding that groups a system's constituents according to their connectivity. This embedding, which reproduces the results of conventional topological diagnostics in established systems, enables a coherent extension of topological phases to complex networks using the Hamiltonian alone, further highlighting exceptional robustness in small-world networks. Our results reshape the conceptual foundations of topological physics by decoupling topological characterization from prescribed physical platforms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29022",
  "author_total": 3,
  "authors": [
    {
      "name": "Sunkyu Yu"
    },
    {
      "name": "Xianji Piao"
    },
    {
      "name": "Namkyoo Park"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4jyac18txsbk2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29022",
  "fulltext_url": null,
  "id": "4jyac18txsbk2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29022",
  "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",
      "physics.optics"
    ],
    [
      "openalex",
      "3107|Topological Materials and Phenomena"
    ]
  ],
  "openalex": "W7223198447",
  "pdf_url": "https://arxiv.org/pdf/2610.29022",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4jyac18txsbk2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.29022",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29022"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Characterizing universal topological phases beyond spatial embedding",
  "title_text": "Characterizing universal topological phases beyond spatial embedding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/4jyac18txsbk2",
  "venue": "arXiv",
  "versions": []
}