Fast algorithm for periodic density fitting for Bloch waves
This work addresses the computational bottleneck of density fitting in electronic structure calculations for periodic systems, offering a faster alternative for researchers in condensed matter physics and materials science.
The paper proposes a fast algorithm for density fitting of Bloch waves in periodic potentials, achieving computational cost scaling as O(N_grid N^2 + N_grid NK log(NK)). Numerical validation in 2D and 3D demonstrates efficiency.
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.