Renormalized perturbation theory for fast evaluation of Feynman diagrams on the real frequency axis

We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but complex renormalization shift. The complex shift acts as a regularization parameter for the numerical integration of otherwise sharp functions. This results in an exponential speed up of stochastic numerical integration at the expense of evaluating additional counterterm diagrams. We provide proof of concept calculations within a difficult limit of the half-filled two-dimensional Hubbard model on a square lattice.

Automated summary

We introduce a method to speed up the numerical evaluation of spatial integrals of Feynman diagrams on the real frequency axis. This is achieved by using a renormalized perturbation expansion with a constant but complex renormalization shift. The complex shift acts as a regularization parameter for the numerical integration of sharp functions, resulting in an exponential speed up of stochastic numerical integration. We provide proof of concept calculations for the difficult limit of the half-filled two-dimensional Hubbard model on a square lattice.