{
  "abstract": "We investigate how spontaneous symmetry breaking and symmetry-protected topology compete and cooperate in one-dimensional quantum spin-1/2 systems. We introduce two families of local Hamiltonians with $\\mathbb{Z}^{\\,}_{2}\\times\\mathbb{Z}^{\\,}_{2}\\times\\mathbb{Z}^{T}_{2}$ symmetry which host a zoo of broken-symmetry phases with and without gapless boundary spins, namely, six long-range-ordered gapped phases that differ by their $\\mathbb{Z}^{\\,}_{2}$-symmetry-breaking patterns (FM$^{\\,}_{x,y,z}$ and Neel$^{\\,}_{x,y,z}$), their partner symmetry-protected topological phases (FM$^{\\mathrm{SPT}}_{x,y}$ and Neel$^{\\mathrm{SPT}}_{x,y}$), and two gapless phases (gFM$^{\\,}_{z}$ and gNeel$^{\\,}_{z}$) with incommensurate $\\mathbb{Z}^{T}_{2}$-breaking magnetic long-range order and central charge $\\mathsf{c}=1$. Direct transitions between competing gapped phases can be continuous or weakly first order. We demonstrate that continuous phase transition lines have exotic critical properties. For example, a line of deconfined quantum critical points (between the Neel$^{\\,}_{x}$ and Neel$^{\\,}_{y}$ phases) described by Tomonaga-Luttinger liquid theory is terminated by the gFM$^{\\,}_{z}$ phase at a Lifshitz tricritical point which exhibits spontaneous breaking of the continuous U(1) symmetry despite the locality and one-dimensionality of the Hamiltonian, contrary to a naive expectation from the Hohenberg-Mermin-Wagner-Coleman theorem. Furthermore, critical lines between symmetry-protected topological phases with different $\\mathbb{Z}^{\\,}_{2}$-symmetry breaking (e.g., Neel$^{\\mathrm{SPT}}_{x}$ and Neel$^{\\mathrm{SPT}}_{y}$) additionally retain low-energy boundary degrees of freedom, realizing symmetry-enriched criticality (or a gapless SPT phase). Our results reveal unconventional mechanisms by which competing symmetry breaking and topology generate ordered critical phases and multicriticality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10694",
  "author_total": 5,
  "authors": [
    {
      "name": "Anthony Rey"
    },
    {
      "name": "Ömer M. Aksoy"
    },
    {
      "name": "Claudio Chamon"
    },
    {
      "name": "Akira Furusaki"
    },
    {
      "name": "Christopher Mudry"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/19rsecbw37431.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10694",
  "fulltext_url": null,
  "id": "19rsecbw37431",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10694",
  "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.str-el"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221102253",
  "pdf_url": "https://arxiv.org/pdf/2610.10694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/19rsecbw37431.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.10694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10694"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Competing symmetry breaking and topology in quantum spin chains",
  "title_text": "Competing symmetry breaking and topology in quantum spin chains",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/19rsecbw37431",
  "venue": "arXiv",
  "versions": []
}