Accidental accuracy and vertex corrections in GW: Exact benchmarks for the extended Hubbard model
Abstract
The GW approximation is the standard tool for quasiparticle predictions in materials, yet its regime of validity in correlated systems remains poorly quantified, because \textit{ab initio} vertex corrections are computationally prohibitive. Using exact diagonalization of the half-filled extended Hubbard model on finite rings as a numerically exact reference, we construct the corresponding model-space GW theory on the identical Hilbert space and quantify its error as a function of local (U) and non-local (V) interaction strength. We find that the required vertex correction changes character across the phase diagram: in the weak-coupling regime the effective vertex Γeff < 1, reflecting the suppression of RPA charge fluctuations by exact short-range correlations, whereas in the Mott regime Γeff grows monotonically (to ∼ 3 at U=8t for N=6), reflecting the local dynamical self-energy structure required to open the Hubbard gap. Vertex corrections in the electron-hole (polarizability) channel are shown to \emph{worsen} the gap error, indicating that reproducing the Mott gap requires dynamical self-energy structure rather than improved screening. For V=0, static COHSEX is accidentally exact at a single crossover U* ≈ 3.5 t; finite V, through non-local Fock exchange, splits this point into a double-crossover window that collapses toward weak coupling. Even at the crossover, however, the exact spectral function retains Hubbard-band structure that no static functional reproduces, so gap agreement does not imply functional accuracy. These results yield quantitative diagnostics for the reliability of GW in correlated materials.
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BibTeX
@misc{atambo2026accidental,
title = {{Accidental accuracy and vertex corrections in $GW$: Exact benchmarks for the extended Hubbard model}},
author = {Michael O. Atambo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.24838},
eprint = {2608.24838},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24838},
}
RIS
TY - UNPB
TI - Accidental accuracy and vertex corrections in GW: Exact benchmarks for the extended Hubbard model
AU - Michael O. Atambo
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2608.24838
UR - https://arxiv.org/abs/2608.24838
AB - The GW approximation is the standard tool for quasiparticle predictions in materials, yet its regime of validity in correlated systems remains poorly quantified, because \textit{ab initio} vertex corrections are computationally prohibitive. Using exact diagonalization of the half-filled extended Hubbard model on finite rings as a numerically exact reference, we construct the corresponding model-space GW theory on the identical Hilbert space and quantify its error as a function of local (U) and non-local (V) interaction strength. We find that the required vertex correction changes character across the phase diagram: in the weak-coupling regime the effective vertex Γ_eff < 1, reflecting the suppression of RPA charge fluctuations by exact short-range correlations, whereas in the Mott regime Γ_eff grows monotonically (to ∼ 3 at U=8t for N=6), reflecting the local dynamical self-energy structure required to open the Hubbard gap. Vertex corrections in the electron-hole (polarizability) channel are shown to \emph{worsen} the gap error, indicating that reproducing the Mott gap requires dynamical self-energy structure rather than improved screening. For V=0, static COHSEX is accidentally exact at a single crossover U^* ≈ 3.5 t; finite V, through non-local Fock exchange, splits this point into a double-crossover window that collapses toward weak coupling. Even at the crossover, however, the exact spectral function retains Hubbard-band structure that no static functional reproduces, so gap agreement does not imply functional accuracy. These results yield quantitative diagnostics for the reliability of GW in correlated materials.
ER -