An Exact Formulation of Phase-Space Electronic Structure Theory in One Dimension by Exploiting the Zero Curvature Condition
Abstract
We show that, for the unique case of a system of electrons and nuclei in one dimension, the hGamma operator in phase space electronic structure theory has a zero non-Abelian curl. Using this fact, we are able to show that a phase space electronic structure framework in Wigner space has a one-to-one mapping to the exact fully quantum vibronic Hamiltonian. In other words, one loses no information by working within the framework of phase space electronic structure theory rather than Born-Huang theory; the only difference is that, whereas Born-Huang theory represents the total vibronic Hamiltonian as a quadratic order expansion in ℏ, the Hamiltonian becomes an infinite order expansion in ℏ within a phase space electronic structure framework (a so-called "Generalized Born-Huang" approach). That being said, numerical results at first or second order demonstrate that, for a limited number of electronic states, phase space electronic structure theory strongly outperforms Born-Huang theory -- a result that justifies a great deal more research into this novel electronic structure approach.
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BibTeX
@misc{zaidi2026exact,
title = {{An Exact Formulation of Phase-Space Electronic Structure Theory in One Dimension by Exploiting the Zero Curvature Condition}},
author = {Zain Zaidi and Yotam M. Y. Feldman and Linqing Peng and Joseph E. Subotnik},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13120},
eprint = {2609.13120},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13120},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Exact Formulation of Phase-Space Electronic Structure Theory in One Dimension by Exploiting the Zero Curvature Condition
AU - Zain Zaidi
AU - Yotam M. Y. Feldman
AU - Linqing Peng
AU - Joseph E. Subotnik
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.13120
UR - https://arxiv.org/abs/2609.13120
AB - We show that, for the unique case of a system of electrons and nuclei in one dimension, the hGamma operator in phase space electronic structure theory has a zero non-Abelian curl. Using this fact, we are able to show that a phase space electronic structure framework in Wigner space has a one-to-one mapping to the exact fully quantum vibronic Hamiltonian. In other words, one loses no information by working within the framework of phase space electronic structure theory rather than Born-Huang theory; the only difference is that, whereas Born-Huang theory represents the total vibronic Hamiltonian as a quadratic order expansion in ℏ, the Hamiltonian becomes an infinite order expansion in ℏ within a phase space electronic structure framework (a so-called "Generalized Born-Huang" approach). That being said, numerical results at first or second order demonstrate that, for a limited number of electronic states, phase space electronic structure theory strongly outperforms Born-Huang theory -- a result that justifies a great deal more research into this novel electronic structure approach.
ER -