Error propagation in the fully self-consistent stochastic second-order Green's function method

TL;DR

This paper introduces a self-consistent stochastic GF2 method that accurately propagates errors during the Dyson equation solution, improving electronic energy calculations without bias.

Contribution

It presents a bias-free, self-consistent stochastic GF2 implementation that effectively manages error propagation in Green's function calculations.

Findings

No systematic bias in electronic energies with the new method

Effective error handling in self-consistent Green's function calculations

Successful tests on simple molecular examples

Abstract

We present an implementation of a fully self-consistent finite temperature second order Green's function perturbation theory (GF2) within the diagrammatic Monte Carlo framework. In contrast to the previous implementations of stochastic GF2 ({\it J. Chem. Phys.},{\bf 151}, 044144 (2019)), the current self-consistent stochastic GF2 does not introduce a systematic bias of the resulting electronic energies. Instead, the introduced implementation accounts for the stochastic errors appearing during the solution of the Dyson equation. We present an extensive discussion of the error handling necessary in a self-consistent procedure resulting in dressed Green's function lines. We test our method on a series of simple molecular examples.