{
  "abstract": "We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called $S^1$-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such $S^1$-family classifications by the exotic symmetry interplay: (i) nontrivial mixed anomalies, (ii) semi-direct product relation between the spontaneously broken and the unbroken symmetries, and (iii) symmetry with noninvertible operators. We find that such structures lead to the novel $S^1$-family classifications inaccessible by earlier classifications based on ``independent'' symmetries. Furthermore, we construct lattice realizations of these $S^1$-families and explicitly demonstrate their novel algebraic structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29915",
  "author_total": 2,
  "authors": [
    {
      "name": "Linhao Li"
    },
    {
      "name": "Yuan Yao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4pjps5bzyb7vg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29915",
  "fulltext_url": null,
  "id": "4pjps5bzyb7vg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29915",
  "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"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7204866846",
  "pdf_url": "https://arxiv.org/pdf/2608.29915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4pjps5bzyb7vg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2608.29915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29915"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Symmetry-Enforced Topological Structures in Quantum Phase Diagrams",
  "title_text": "Symmetry-Enforced Topological Structures in Quantum Phase Diagrams",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/4pjps5bzyb7vg",
  "venue": "arXiv",
  "versions": []
}