Efficient Deterministic-Stochastic Representation of the Coulomb Operator in Real Space
Abstract
We present an efficient mixed deterministic-stochastic approach for constructing the Coulomb operator in real space that preserves accuracy across the full spectral range. The dominant long-range components of the interaction are captured deterministically via a compact, low-rank approximation, constructed using Chebyshev-filtered subspace iteration, while the remaining spectral tail is treated using unbiased probing with a small number of stochastic vectors. The resulting operator is benchmarked within self-consistent field calculations for the extended Hubbard Hamiltonian on periodic, perturbed, and non-periodic three-dimensional lattices. We account for stochastic bias in observables by implementing a jackknife correction. The method systematically improves with deterministic rank and stochastic sample count, while substantially reducing the computational cost of constructing the Coulomb matrix.
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BibTeX
@misc{faiaz2026efficient,
title = {{Efficient Deterministic-Stochastic Representation of the Coulomb Operator in Real Space}},
author = {Nafiz Faiaz and Tucker Allen and Dimitri Bazile and Kajsa Williams and Daniel Neuhauser},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10189},
eprint = {2609.10189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10189},
}
RIS
TY - UNPB
TI - Efficient Deterministic-Stochastic Representation of the Coulomb Operator in Real Space
AU - Nafiz Faiaz
AU - Tucker Allen
AU - Dimitri Bazile
AU - Kajsa Williams
AU - Daniel Neuhauser
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10189
UR - https://arxiv.org/abs/2609.10189
AB - We present an efficient mixed deterministic-stochastic approach for constructing the Coulomb operator in real space that preserves accuracy across the full spectral range. The dominant long-range components of the interaction are captured deterministically via a compact, low-rank approximation, constructed using Chebyshev-filtered subspace iteration, while the remaining spectral tail is treated using unbiased probing with a small number of stochastic vectors. The resulting operator is benchmarked within self-consistent field calculations for the extended Hubbard Hamiltonian on periodic, perturbed, and non-periodic three-dimensional lattices. We account for stochastic bias in observables by implementing a jackknife correction. The method systematically improves with deterministic rank and stochastic sample count, while substantially reducing the computational cost of constructing the Coulomb matrix.
ER -