Spatial-Order Hierarchy of Time-Dependent Exchange-Correlation Potential
Abstract
Exact time-dependent density-functional theory (DFT) separates the exchange-correlation potential into interaction and kinetic-correlation components, but the structural relation between them remains unclear. We establish a representability constraint based on the off-diagonal expansion of the one-electron reduced density matrix (1RDM) relative to a chosen reference dynamics. A non-zero linear off-diagonal term of the 1RDM generates a current density beyond the representable space of the reference, while a nontrivial quadratic off-diagonal structure activates the kinetic-correlation component. The resulting hierarchy provides a criterion for assessing, from the spatial locality of electronic correlation, whether a given exchange-correlation functional or a more general electron-correlation approximation remains adequate. In a one-dimensional two-electron correlation quench, retaining the exact interaction component while setting the kinetic component to zero suppresses the density broadening of the exact evolution. These results establish a spatial-order hierarchy among the force components governing the density dynamics and provide an exact constraint for the construction and assessment of nonadiabatic approximations.
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BibTeX
@misc{negishi2026spatialorder,
title = {{Spatial-Order Hierarchy of Time-Dependent Exchange-Correlation Potential}},
author = {Naoki Negishi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.01483},
eprint = {2608.01483},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.01483},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Spatial-Order Hierarchy of Time-Dependent Exchange-Correlation Potential
AU - Naoki Negishi
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2608.01483
UR - https://arxiv.org/abs/2608.01483
AB - Exact time-dependent density-functional theory (DFT) separates the exchange-correlation potential into interaction and kinetic-correlation components, but the structural relation between them remains unclear. We establish a representability constraint based on the off-diagonal expansion of the one-electron reduced density matrix (1RDM) relative to a chosen reference dynamics. A non-zero linear off-diagonal term of the 1RDM generates a current density beyond the representable space of the reference, while a nontrivial quadratic off-diagonal structure activates the kinetic-correlation component. The resulting hierarchy provides a criterion for assessing, from the spatial locality of electronic correlation, whether a given exchange-correlation functional or a more general electron-correlation approximation remains adequate. In a one-dimensional two-electron correlation quench, retaining the exact interaction component while setting the kinetic component to zero suppresses the density broadening of the exact evolution. These results establish a spatial-order hierarchy among the force components governing the density dynamics and provide an exact constraint for the construction and assessment of nonadiabatic approximations.
ER -