Putting a Temperature on Electron Correlation
Abstract
It is common wisdom that a better understanding of how to quantify electron correlation should lead to more efficient treatments of the correlation problem. Here, we not only substantiate this view but turn it into a concrete, systematic framework for ground states. Since prominent correlation measures such as the nonfreeness depend only on the one-particle reduced density matrix, modeling the correlation energy as a function of such a measure naturally places the framework within reduced density matrix functional theory, while keeping the cost at mean-field level. Strikingly, the variable conjugate to the measure emerges as a ``correlation temperature'', thereby connecting correlation measures, functional theory, and effective temperatures. The framework rationalizes methods such as i-DMFT, and we illustrate its key concepts analytically for the Hubbard dimer and numerically for small molecular systems. This brings a fundamental question within reach: how much of the correlation problem can be solved at mean-field cost?
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BibTeX
@misc{graf2026putting,
title = {{Putting a Temperature on Electron Correlation}},
author = {Paul G. Graf and Florian Matz and Markus Penz and Christian Schilling},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22134},
eprint = {2610.22134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22134},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Putting a Temperature on Electron Correlation
AU - Paul G. Graf
AU - Florian Matz
AU - Markus Penz
AU - Christian Schilling
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22134
UR - https://arxiv.org/abs/2610.22134
AB - It is common wisdom that a better understanding of how to quantify electron correlation should lead to more efficient treatments of the correlation problem. Here, we not only substantiate this view but turn it into a concrete, systematic framework for ground states. Since prominent correlation measures such as the nonfreeness depend only on the one-particle reduced density matrix, modeling the correlation energy as a function of such a measure naturally places the framework within reduced density matrix functional theory, while keeping the cost at mean-field level. Strikingly, the variable conjugate to the measure emerges as a ``correlation temperature'', thereby connecting correlation measures, functional theory, and effective temperatures. The framework rationalizes methods such as i-DMFT, and we illustrate its key concepts analytically for the Hubbard dimer and numerically for small molecular systems. This brings a fundamental question within reach: how much of the correlation problem can be solved at mean-field cost?
ER -