{
  "abstract": "We study the localization of a quantum particle in a one-dimensional disordered system with long-range hopping amplitudes $t(r)\\propto r^{-a}$. In contrast to the standard one-dimensional Anderson model ($a\\to\\infty$), in which all states are localized and the localization length is minimal at the band edge, the long-range model with $1<a<3/2$ exhibits a disorder-driven transition at the band edge, while high-energy states remain localized at arbitrary disorder strength. We investigate this transition for the ground state in momentum space. In the weak-disorder regime, we derive perturbative expressions for the characteristic functions and moments of the momentum-space wave function, as well as for its fractal dimensions. Our results demonstrate that the ground state exhibits $\\it semilocalization$ rather than conventional localization, thereby extending the class of models displaying the unusual $\\it semifractality$ of wave functions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.25806",
  "author_total": 5,
  "authors": [
    {
      "name": "Murod S. Bahovadinov"
    },
    {
      "name": "Faridun N. Jalolov"
    },
    {
      "name": "Vladimir E. Kravtsov"
    },
    {
      "name": "Boris L. Altshuler"
    },
    {
      "name": "Georgy V. Shlyapnikov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0xp34mddszkfk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.25806",
  "fulltext_url": null,
  "id": "0xp34mddszkfk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.25806",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7204460893",
  "pdf_url": "https://arxiv.org/pdf/2608.25806",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0xp34mddszkfk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2608.25806",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.25806"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Semi-localized ground state in a 1D system with long-range hopping",
  "title_text": "Semi-localized ground state in a 1D system with long-range hopping",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/0xp34mddszkfk",
  "venue": "arXiv",
  "versions": []
}