Stochastic resolution of identity to second order Green’s function: ground-state and quasi-particle properties.

We develop a stochastic resolution of identity approach to the real-time second-order Green’s function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green’s function (J. Chem. Phys.151, 044114 (2019)). The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies as well as predict ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments and to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal scaling toO(N^3), where N is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe as lightly lower than cubic scaling for systems containing up to N≈1000.