We present low-scaling algorithms for GW and constrained random phase approximation based on a symmetry-adapted interpolative separable density fitting (ISDF) procedure that incorporates the space-group symmetries of crystalline systems. The resulting formulations scale cubically with respect to system sizes and linearly with the number of k-points, regardless of the choice of single-particle basis and whether a quasiparticle approximation is employed. We validate these methods through comparisons with published literature and demonstrate their efficiency in treating large-scale systems through the construction of downfolded many-body Hamiltonians for carbon dimer defects embedded in hexagonal boron nitride supercells. Our work highlights the efficiency and general applicability of ISDF in the context of large-scale many-body calculations with k-point sampling beyond density functional theory.
@article{arxiv.2401.12308,
title = {Low-Scaling algorithms for $GW$ and constrained random phase approximation using symmetry-adapted interpolative separable density fitting},
author = {Chia-Nan Yeh and Miguel A. Morales},
journal= {arXiv preprint arXiv:2401.12308},
year = {2024}
}