Calculating the self-energy of the 2d Hubbard model with Diagrammatic Monte Carlo and Algorithmic Matsubara Integration

We have self-consistently calculated the self-energy of the 2d Hubbard model using diagrammatic Monte Carlo to evaluate the diagrammatic series to high order and Algorithmic Matsubara Integration to perform the Matsubara integrals. The symbollic integration of the Matsubara frequencies makes the real frequency dependence of the self-energy accessible with trivial analytic continuation. We use the spectral representation of the Green's functions to calculate the perturbative series with a starting point away from U=0 and so can perform calculations when U=0 is a singular point.