{
  "abstract": "What quantum mutual information adds to conventional correlation functions is often unclear. We study the spin-1/2 $J_1$-$J_2$ Heisenberg chain, using DMRG on infinite chains and periodic rings and an SU(2) decomposition of the mutual information into correlation channels. For singlet ground states the two-site mutual information is an exact function of the spin correlator, so any additional content must come from blocks. In the dimerized phase, blocks resolve bond-energy correlations in the SU(2)-scalar channel without an independent asymptotic length: singlet and triplet correlation lengths agree to about 1%. The scalar channel dominates block mutual information at large distances in the commensurate regime up to $J_2/J_1=0.40$, but falls to a few percent beyond the disorder point, which coincides numerically with the Majumdar-Ghosh point $J_2/J_1=1/2$; the structure-factor peak splits only at the Lifshitz point $J_2/J_1=0.520622(2)$. On the gapless side we compare block mutual information on rings extrapolated to infinite size with the two-interval prediction of SU(2)$_1$ conformal field theory across the Kosterlitz-Thouless point $J_2/J_1=0.241167$. There, for block lengths $l\\le6$, the correction decays as $l^{-p}$ with $p=1.96$-$2.07$, and any logarithmic term is at least 60 times smaller than in the Heisenberg chain. Expanding in the marginal coupling (from level spectroscopy) the first-order coefficient is consistent with $l^{-2}$ scaling and the second-order coefficient is positive for $x\\le1/4$, suggesting that the mutual information relative to the field-theory value becomes stationary at the KT point for large blocks. The scalar-channel share approaches 1/4 at small cross ratio $x$, as expected from SO(4) symmetry; under two stated assumptions its first-order response to the coupling is $(3/8)\\ln x-5/8$ at small $x$, matched by the $l=4$ data within 1-3% at $x\\le1/9$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16915",
  "author_total": 2,
  "authors": [
    {
      "name": "Wuttichai Pankeaw"
    },
    {
      "name": "Pruet Kalasuwan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/90gbxakbkc9x6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16915",
  "fulltext_url": null,
  "id": "90gbxakbkc9x6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16915",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221814017",
  "pdf_url": "https://arxiv.org/pdf/2610.16915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/90gbxakbkc9x6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:06Z",
      "native_id": "2610.16915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16915"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Mutual information across the commensurate--incommensurate crossover and near the Kosterlitz--Thouless point of the spin-$\\tfrac12$ $J_1$--$J_2$ Heisenberg chain",
  "title_text": "Mutual information across the commensurate--incommensurate crossover and near the Kosterlitz--Thouless point of the spin-1/2 J_1--J_2 Heisenberg chain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:06Z",
  "url": "https://research.draconitic.com/paper/90gbxakbkc9x6",
  "venue": "arXiv",
  "versions": []
}