Stochastic self-consistent Green's function second-order perturbation theory (sGF2)

TL;DR

This paper introduces a stochastic version of the GF2 method, significantly reducing computational cost while maintaining accuracy for electronic structure calculations of correlated systems.

Contribution

The authors develop sGF2, a stochastic approach to GF2 that scales quasi linearly with system size, enabling efficient and accurate large-scale electronic structure computations.

Findings

sGF2 achieves small stochastic errors (~0.05%) in correlation energy.

The method scales quasi linearly with system size.

sGF2 automatically provides temperature-dependent MP2 energies.

Abstract

The second-order Green's function method (GF2) was shown recently to be an accurate self-consistent approach for electronic structure of correlated systems since the self-energy accounts for both the weak and some of the strong correlation. The numerical scaling of GF2 is quite steep however, $O({N^5})$ (where the pre-factor is often hundreds), effectively preventing its application to large systems. Here, we develop a stochastic approach to GF2 (sGF2) where the self-energy is evaluated by a random-vector decomposition of Green's functions so that the dominant part of the calculation scales quasi linearly with system size. A study of hydrogen chains shows that the resulting approach is numerically efficient and accurate, as the stochastic errors are very small, 0.05% of the correlation energy for large systems with only a moderate computational effort. The method also yields automatically efficient MP2 energies and is automatically temperature dependent.