High order corrections to the GW approximation for the 2D Hubbard model

In conventional GW approximation scheme the effective screened interaction is usually restricted at RPA level. We extend this to include arbitrarily high order Feynman diagrams in the 2D Hubbard model. We utilize Algorithmic Matsubara Integration to symbolically generate analytical expressions and evaluate the Matsubara sums via standard Monte Carlo. We construct an infinite resummation scheme that resolves the instability associated with Q = (π, π) region common in low order resummation schemes.