Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis

TL;DR

This paper introduces a renormalized perturbation approach with a complex shift to significantly speed up the numerical evaluation of Feynman diagrams on the real frequency axis, demonstrated on the 2D Hubbard model.

Contribution

The method provides a novel way to accelerate Feynman diagram evaluations using a complex renormalization shift, improving computational efficiency.

Findings

Exponential speed-up in stochastic numerical integration.

Effective regularization of sharp functions on the real frequency axis.

Successful application to the half-filled 2D Hubbard model.

Abstract

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 counter-term diagrams. We provide proof of concept calculations within a difficult limit of the half-filled 2D Hubbard model on a square lattice.