Contact Renormalization of One-Mode Electron Correlation: Validation in Four- and Ten-Electron Systems
Abstract
A stationary many-electron eigenstate has one dynamical phase although its internal response can be strongly multimode. We ask whether the stationary Hartree--Fock information carrier contains enough information to determine the scalar correlation energy through one effective return. In regularized Hartree--Fock, Gaussian primitive products fix a minimum-information relative-coordinate mode before any one-mode reduction; virial completion defines the correlation source, while exact contact measures the additional return restriction created by neighboring occupied pairs. The Be-like 1s22s2 sequence establishes the one-valence-pair boundary: with no neighboring occupied valence pair, the source returns through the universal floor D0=√(1+δ2). Ten-electron molecules and Ne-like ions then test how finite-pair contact dresses that return. The same parameter-free source--return construction reproduces the established molecular and ionic correlation trends with quantitative accuracy. The numerical agreement therefore serves as validation of a physical separation between source strength and return restriction, rather than as the objective by itself.
Related
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BibTeX
@misc{panas2026contact,
title = {{Contact Renormalization of One-Mode Electron Correlation: Validation in Four- and Ten-Electron Systems}},
author = {Itai Panas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31031},
eprint = {2610.31031},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31031},
}
RIS
TY - UNPB
TI - Contact Renormalization of One-Mode Electron Correlation: Validation in Four- and Ten-Electron Systems
AU - Itai Panas
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.31031
UR - https://arxiv.org/abs/2610.31031
AB - A stationary many-electron eigenstate has one dynamical phase although its internal response can be strongly multimode. We ask whether the stationary Hartree--Fock information carrier contains enough information to determine the scalar correlation energy through one effective return. In regularized Hartree--Fock, Gaussian primitive products fix a minimum-information relative-coordinate mode before any one-mode reduction; virial completion defines the correlation source, while exact contact measures the additional return restriction created by neighboring occupied pairs. The Be-like 1s^22s^2 sequence establishes the one-valence-pair boundary: with no neighboring occupied valence pair, the source returns through the universal floor D_0=√(1+δ^2). Ten-electron molecules and Ne-like ions then test how finite-pair contact dresses that return. The same parameter-free source--return construction reproduces the established molecular and ionic correlation trends with quantitative accuracy. The numerical agreement therefore serves as validation of a physical separation between source strength and return restriction, rather than as the objective by itself.
ER -