Enabling 13K-Atom Excited-State GW Calculations via Low-Rank Approximations and HPC on the New Sunway Supercomputer

GW approximation is a powerful approach to accurately describe the excited-state of semiconductors. However, GW incurs high computational cost $\mathcal{O}\left(N^{4}\right)$ and large memory usage $\mathcal{O}\left(N^{3}\right)$, limiting its applications to thousands of (2,742) atoms even on leadership supercomputers. Herein we present a massively parallel implementation of accurate and efficient cubic-scaling plane-wave GW calculations by using low-rank approximations and high-performance computing on leadership supercomputers. By using a series of low rank approximations, we can reduce the expensive GW calculations to the cubic-scaling computational cost $\mathcal{O}\left(N^{3}\right)$ and quadratic memory usage $\mathcal{O}\left(N^{2}\right)$. With the help of parallel and communication optimization, the plane-wave GW calculations gain an overall speedup of over 70x and efficiently scale up to 13,824 atoms within a few minutes using 449,280 cores on new Sunway supercomputer. This accomplishment paves the way for excited-state quantum mechanical material simulations at mesoscopic scale (10K atoms) and for the design of next-generation semiconductor devices.