V-Representability Beyond Singular Times in Time-Dependent Density Functional Theory: The Hubbard Dimer Case
Abstract
We study the global V-representability problem in time-dependent density functional theory (TDDFT) for the two-particle Hubbard dimer model in the spin-singlet sector. In particular, we investigate whether the time-dependent density of the interacting system obtained for a given one-body external potential u (the tunable control variable) can be reproduced by a non-interacting Kohn--Sham system beyond the singular times at which the usual inversion formulas break down. We deal with both the conventional formulation of TDDFT based on some time-dependent variational principle and the recently introduced geometric formulation of TDDFT (Phys. Rev. Lett. 136 (2026) 256401, Phys. Rev. A 113 (2026) 062222). For both principles, we prove global-in-time V-representability, show that singular times induce non-uniqueness of the time-dependent effective potential, and classify the set of solutions.
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BibTeX
@misc{cances2026vrepresentability,
title = {{V-Representability Beyond Singular Times in Time-Dependent Density Functional Theory: The Hubbard Dimer Case}},
author = {Éric Cancès and Théo Duez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33837},
eprint = {2610.33837},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33837},
}
RIS
TY - UNPB
TI - V-Representability Beyond Singular Times in Time-Dependent Density Functional Theory: The Hubbard Dimer Case
AU - Éric Cancès
AU - Théo Duez
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33837
UR - https://arxiv.org/abs/2610.33837
AB - We study the global V-representability problem in time-dependent density functional theory (TDDFT) for the two-particle Hubbard dimer model in the spin-singlet sector. In particular, we investigate whether the time-dependent density of the interacting system obtained for a given one-body external potential u (the tunable control variable) can be reproduced by a non-interacting Kohn--Sham system beyond the singular times at which the usual inversion formulas break down. We deal with both the conventional formulation of TDDFT based on some time-dependent variational principle and the recently introduced geometric formulation of TDDFT (Phys. Rev. Lett. 136 (2026) 256401, Phys. Rev. A 113 (2026) 062222). For both principles, we prove global-in-time V-representability, show that singular times induce non-uniqueness of the time-dependent effective potential, and classify the set of solutions.
ER -