{
  "abstract": "We investigate the structure of effective Hamiltonians governing monitored dynamics of a one-dimensional Majorana chain using Lyapunov spectral analysis. We focus on the gapless phase of the Lyapunov spectrum, where the effective Hamiltonians behave differently from conventional critical Hamiltonians in isolated systems; the spectral gap closes faster than $1/L$ but slower than $1/L^2$ and the entanglement entropy grows as $[\\ln(L)]^2$ where $L$ is the system size. We find that the effective Hamiltonians have random long-range power-law hoppings with nontrivial magnitude correlations, rather than being independently and identically distributed. To elucidate the role of these non-Gaussian correlations, we construct random power-law hopping models that capture the essential features of the effective Hamiltonians. The spectral gaps of the constructed models decay faster than $1/L$ but slower than $1/L^2$. We find that, in the absence of hopping correlations, the ground-state entanglement exhibits $\\ln(L)$ scaling. In the presence of correlations, by contrast, the entanglement entropy is enhanced and its system-size dependence is consistent with $[\\ln(L)]^2$ scaling over the system sizes studied. These results suggest that correlations among long-range hopping magnitudes are responsible for the entanglement scaling rarely encountered in the ground states of conventional isolated quantum systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04091",
  "author_total": 4,
  "authors": [
    {
      "name": "Ken Mochizuki"
    },
    {
      "name": "Hisanori Oshima"
    },
    {
      "name": "Ryusuke Hamazaki"
    },
    {
      "name": "Yohei Fuji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8c98b4jpske0g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04091",
  "fulltext_url": null,
  "id": "8c98b4jpske0g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04091",
  "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"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7208792528",
  "pdf_url": "https://arxiv.org/pdf/2609.04091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8c98b4jpske0g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2609.04091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04091"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling",
  "title_text": "Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:35Z",
  "url": "https://research.draconitic.com/paper/8c98b4jpske0g",
  "venue": "arXiv",
  "versions": []
}