Accidental accuracy and formal consistency in GW+BSE: Exact benchmarks and regime-dependent error cancellation
Abstract
Standard many-body perturbation theory for optical excitations combines the GW approximation for quasiparticle energies with the Bethe-Salpeter equation (BSE) for the electron-hole response. Formally, the BSE kernel must equal the functional derivative of the self-energy, K=δΣ/δG. In routine practice, however, the kernel is built from a statically screened direct interaction and a bare exchange interaction, which breaks this consistency. Using exact diagonalization of the extended Hubbard dimer, we construct a controlled benchmark that isolates the price of this inconsistency. We show that the internally inconsistent practical GW+BSE construction frequently yields accurate optical gaps through accidental cancellation between an underestimated GW gap and an oversized bare-exchange kernel, and we map the regions of parameter space where this accidental accuracy occurs. Upon switching on the nearest-neighbor interaction and binding the exciton, the practical construction remains the accurate one throughout the weak-binding regime, with cancellation optima at parts in 103, while the frozen-W construction fails at every binding strength. Beyond a binding threshold both static constructions deteriorate, showing that deeply bound excitons require physics beyond any static kernel. Accidental accuracy is therefore a property of the weak-binding regime, and the systematic failure of the frozen-W derivative kernel within the explored parameter space traces to its overscreening of the exchange channel. The accuracy of the practical kernel is an accidental cancellation of two independent errors, an underestimated quasiparticle gap and an oversized exchange term, not a hidden consistency. These results provide a controlled taxonomy of approximation failure in GW+BSE and a precise diagnostic for when standard workflows can be trusted.
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BibTeX
@misc{atambo2026accidental,
title = {{Accidental accuracy and formal consistency in $GW$+BSE: Exact benchmarks and regime-dependent error cancellation}},
author = {Michael O. Atambo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38247},
eprint = {2609.38247},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38247},
}
RIS
TY - UNPB
TI - Accidental accuracy and formal consistency in GW+BSE: Exact benchmarks and regime-dependent error cancellation
AU - Michael O. Atambo
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38247
UR - https://arxiv.org/abs/2609.38247
AB - Standard many-body perturbation theory for optical excitations combines the GW approximation for quasiparticle energies with the Bethe-Salpeter equation (BSE) for the electron-hole response. Formally, the BSE kernel must equal the functional derivative of the self-energy, K=δΣ/δG. In routine practice, however, the kernel is built from a statically screened direct interaction and a bare exchange interaction, which breaks this consistency. Using exact diagonalization of the extended Hubbard dimer, we construct a controlled benchmark that isolates the price of this inconsistency. We show that the internally inconsistent practical GW+BSE construction frequently yields accurate optical gaps through accidental cancellation between an underestimated GW gap and an oversized bare-exchange kernel, and we map the regions of parameter space where this accidental accuracy occurs. Upon switching on the nearest-neighbor interaction and binding the exciton, the practical construction remains the accurate one throughout the weak-binding regime, with cancellation optima at parts in 10^3, while the frozen-W construction fails at every binding strength. Beyond a binding threshold both static constructions deteriorate, showing that deeply bound excitons require physics beyond any static kernel. Accidental accuracy is therefore a property of the weak-binding regime, and the systematic failure of the frozen-W derivative kernel within the explored parameter space traces to its overscreening of the exchange channel. The accuracy of the practical kernel is an accidental cancellation of two independent errors, an underestimated quasiparticle gap and an oversized exchange term, not a hidden consistency. These results provide a controlled taxonomy of approximation failure in GW+BSE and a precise diagnostic for when standard workflows can be trusted.
ER -