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Analytical results for the Shannon entropy of the critical transverse-field Ising chain — arXiv:2610.08591

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.08591
License (as archived): CC0-1.0
Archived: 2026-10-07T15:29:31.962Z
SHA-256 of the archived text: 3c6166508f691c8df437afb3fe6dc761416ddc14d2e9115d632ac2dbf81ac464
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Analytical results for the Shannon entropy of the critical transverse-field Ising chain — arXiv:2610.08591 — arXiv (en), https://arxiv.org/abs/2610.08591 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_0c183e86fcbb (Metraipolis archive dc_0c183e86fcbb, sha256 3c6166508f691c8df437afb3fe6dc761416ddc14d2e9115d632ac2dbf81ac464)

BibTeX

@misc{dc0c183e86fcbb,
  title = {Analytical results for the Shannon entropy of the critical transverse-field Ising chain — arXiv:2610.08591},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.08591},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_0c183e86fcbb; sha256 3c6166508f691c8df437afb3fe6dc761416ddc14d2e9115d632ac2dbf81ac464},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.08591. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Local-basis Shannon entropies of critical wave functions contain universal subleading information, but the Shannon point of the critical transverse-field Ising chain is singular in the conventional Rényi approach. We treat it directly at $n=1$ by representing the complete computational-basis Born distribution as the odd-degree boundary of independent long-range Bernoulli edges. The Shannon chain rule separates the entropy into explicit independent-edge and conditional cycle-space terms. For the periodic chain this isolates the analytic edge anomaly and organizes the remaining constant by linked vertex support. Conditional on the stated finite-part matching and forest assumptions, every nonvanishing linked coefficient is represented by an explicit finite-dimensional integral, giving an all-orders analytic hierarchy; the four-vertex term is evaluated in closed form, and the first few linked sectors already nearly saturate the established periodic constant, which is also reconstructed independently from the exact finite-size distribution. For an interval, the exterior reduces exactly to one ghost vertex and the explicit squared logarithms cancel, leaving the analytic edge contribution $\gamma_E=\log2/4-1/16$. The conditional cycle term has an exact all-support decomposition into physical-line and ghost-linked sectors; conditional on closure of the boundary forest subtraction, these sectors define an all-orders hierarchy of renormalized line and monomer--dimer boundary periods for the remaining logarithmic coefficient. The first complete augmented linked coefficient is evaluated in closed form, with an exact cancellation between its line and ghost boundary-layer anomalies; an independent reconstruction from exact finite-size probabilities recovers the established coefficient $\gamma_1=0.060020(3)$.

Tema degli esploratori: fisica e astronomia (elenco arXiv quant-ph, nuovi lavori del giorno).
Categorie arXiv: Statistical Mechanics (cond-mat.stat-mech) ; Mathematical Physics (math-ph); Quantum Physics (quant-ph).
Pagina del lavoro: https://arxiv.org/abs/2610.08591 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T15:00:59.498Z dalla pagina https://arxiv.org/list/quant-ph/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).