Hierarchical Fourier Phase Projection for Local Electronic Observables
Abstract
Large-scale electronic-structure calculations require efficient access to local observables without explicitly constructing all occupied orbitals. We develop hierarchical Fourier phase projection (HPP), which organizes Fourier probes into a reusable spatial hierarchy that progressively removes short-range aliasing while exploiting density-matrix locality. The method provides systematic refinement from low-cost local estimates to the projection-exact limit of the chosen numerical occupation operator, without discarding previously evaluated responses. Tests using frozen Kohn--Sham Hamiltonians for semiconducting and metallic systems demonstrate controllable convergence of electron densities and nonlocal pseudopotential forces, weak size dependence of the probing resolution required for a fixed local accuracy, and near-linear growth of the direct computational cost at fixed probing workload. Inter-level changes further provide practical information for terminating the refinement at finite accuracy. HPP connects electronic locality, observable accuracy, and computational effort within a single hierarchical framework, providing a scalable route to local quantities in large-scale electronic-structure calculations.
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BibTeX
@misc{hu2026hierarchical,
title = {{Hierarchical Fourier Phase Projection for Local Electronic Observables}},
author = {Tao Hu and Weiqing Zhou and Zhichang Fu and Yechen Chen and Shengjun Yuan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37814},
eprint = {2609.37814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37814},
}
RIS
TY - UNPB
TI - Hierarchical Fourier Phase Projection for Local Electronic Observables
AU - Tao Hu
AU - Weiqing Zhou
AU - Zhichang Fu
AU - Yechen Chen
AU - Shengjun Yuan
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37814
UR - https://arxiv.org/abs/2609.37814
AB - Large-scale electronic-structure calculations require efficient access to local observables without explicitly constructing all occupied orbitals. We develop hierarchical Fourier phase projection (HPP), which organizes Fourier probes into a reusable spatial hierarchy that progressively removes short-range aliasing while exploiting density-matrix locality. The method provides systematic refinement from low-cost local estimates to the projection-exact limit of the chosen numerical occupation operator, without discarding previously evaluated responses. Tests using frozen Kohn--Sham Hamiltonians for semiconducting and metallic systems demonstrate controllable convergence of electron densities and nonlocal pseudopotential forces, weak size dependence of the probing resolution required for a fixed local accuracy, and near-linear growth of the direct computational cost at fixed probing workload. Inter-level changes further provide practical information for terminating the refinement at finite accuracy. HPP connects electronic locality, observable accuracy, and computational effort within a single hierarchical framework, providing a scalable route to local quantities in large-scale electronic-structure calculations.
ER -