Stochastic Resolution of Identity for Real-Time Second-Order Green's Function: Ionization Potential and Quasi-particle Spectrum

TL;DR

This paper introduces a stochastic method for real-time Green's function calculations that accurately predicts ionization potentials and spectra, with reduced computational scaling suitable for large molecules.

Contribution

The authors develop a stochastic resolution of identity approach for real-time second-order Green's function theory, enabling efficient and accurate spectral predictions.

Findings

Achieves accuracy comparable to self-consistent GW.

Reduces computational scaling to approximately O(N_e^3).

Demonstrates applicability to large molecular systems with up to 1000 electrons.

Abstract

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 {\em J. Chem. Phys.} {\bf 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 to $O(N_e^3)$, where $N_e$ is the number of electrons. This is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to $N_e \approx 1000$.