Compression for GW perturbation theory calculations via tensor rank decomposition

GW perturbation theory (GWPT) [1] is an ab initio linear-response method to compute electron-phonon (e-ph) coupling matrix elements that include many-electron self-energy effects at the GW level. However, large-scale or systematic studies using GWPT are highly demanding due to the computational expense of calculating the GW self-energy corrections to the numerous e-ph matrix elements that are needed in physical studies. In this talk, we present a method to reduce the cost of GWPT based on tensor rank decomposition, a widely used compression technique for high-dimensional data. This method allows us to obtain properties such as the e-ph coupling constant λ to high accuracy for much lower computational cost, as the full GW self-energy correction matrix is replaced by a low-rank approximation requiring only a small fraction of all terms to be computed.

[1] Li, Antonius, Wu, da Jornada, and Louie, Phys. Rev. Lett. 122, 186402 (2019).