Year: 2026
Type: preprint
Abstract: In this letter, we develop hierarchical Fourier phase projection (HPP) for the calculation of local electronic observables. The method couples the spatial decay of the density matrix with a hierarchy of Fourier probes, improving accuracy through refinement, and making use of all previously evaluated responses. The variation in the calculated observables during the refinement process carries information on the residual error. We use a locality-based model to estimate the error from these changes with no extra probing calculations. In particular, we demonstrate the method for electron densities and nonlocal pseudopotential forces for fixed Kohn-Sham Hamiltonians of semiconductors, metals and thermally perturbed silica. The convergence is significantly accelerated by the spatial decay of the density matrix, especially if the density matrix is short-ranged. The number of probes necessary to achieve a specific local accuracy is only weakly dependent on the system size within the range of consideration. HPP provides a route toward linear-scaling electronic-structure calculations in which the computational effort for local observables can be matched to the required accuracy, offering an error-aware strategy for large-scale first-principles simulations.
Source: arXiv (Cornell University)
Institutions: Wuhan University, Wuhan Institute of Quantum Technology
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G465544519, G6151145709
OpenAlex ID: W7214909884