Fast algorithm for periodic density fitting for Bloch waves

TL;DR

This paper introduces a fast, scalable algorithm for density fitting of Bloch waves in periodic systems, significantly reducing computational costs for electronic structure calculations.

Contribution

The paper presents a novel density fitting algorithm based on column selection and random Fourier projection, improving efficiency for periodic Hamiltonian operators.

Findings

Computational cost scales as O(N_grid N^2 + N_grid N K log(NK)).

Validated with numerical examples in 2D and 3D.

Efficient for large-scale periodic systems.

Abstract

We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The computational cost of the algorithm scales as $\mathcal{O}\bigl(N_{\text{grid}} N^2 + N_{\text{grid}} NK \log (NK)\bigr)$, where $N_{\text{grid}}$ is number of spatial grid points, $K$ is the number of sampling $k$-points in first Brillouin zone, and $N$ is the number of bands under consideration. We validate the algorithm by numerical examples in both two and three dimensions.