{
  "abstract": "Nonlocal magic quantifies the minimum nonstabilizerness attainable under independent local unitary transformations on the two subsystems. Here, we use min-relative nonlocal magic (NLM) to characterize the crossover from ergodicity to many-body localization (MBL) in the random-field XXZ chain. Unlike entanglement entropy, NLM probes how entanglement is organized through the distance of the Schmidt spectrum from dyadic-flat stabilizer spectra. From weak to intermediate disorder, NLM evolves from an $O(1)$ Haar-like value into a size-enhanced dome, while entanglement remains volume-law, revealing a spectral reorganization not visible in the entropy. Deep in the MBL regime, a two-level cut-hybridization model captures the nearly binary Schmidt spectrum and explains why the mean and median NLM decay approximately as $W^{-1}$ and $W^{-2}$, respectively. Following a product-state quench, NLM overshoots and relaxes in the ergodic regime, whereas at strong disorder it grows slowly and approximately logarithmically. These results show that NLM resolves Schmidt-spectrum structure not visible in the entanglement entropy and provides a complementary probe of ergodicity breaking.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16935",
  "author_total": 2,
  "authors": [
    {
      "name": "Shan-Zhong Li"
    },
    {
      "name": "Zhi Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2p6y1ftzxpfxt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16935",
  "fulltext_url": null,
  "id": "2p6y1ftzxpfxt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16935",
  "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.dis-nn"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7213391374",
  "pdf_url": "https://arxiv.org/pdf/2609.16935",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2p6y1ftzxpfxt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16935",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16935"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Nonlocal Magic across the Many-Body Localization Crossover",
  "title_text": "Nonlocal Magic across the Many-Body Localization Crossover",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:41Z",
  "url": "https://research.draconitic.com/paper/2p6y1ftzxpfxt",
  "venue": "arXiv",
  "versions": []
}