Self-consistent summation of many-particle diagrams on the real frequency axis and its application to the FLEX approximation

Abstract

A new numerical method for the summation of Greens function diagrams on the real frequency axis is presented. We apply our approach to the fluctuation exchange approximation for the two-dimensional Hubbard model, thereby taking full account of the momentum and frequency dependence of the Greens functions and the resulting interactions. Using the contour deformation technique in the complex frequency plane, the self-energy integrals are evaluated by a combination of Fourier and Laplace transformation and a subsequent application of the Fast Fourier Transformation. In contrast to the imaginary frequency approach, this method gives direct access to dynamical properties with high energy resolution and good numerical stability. Results for the electronic spectral density are shown which exhibit new fine structure within the elementary excitations and in particular the shadows of the Fermi surface, recently observed in high- T c superconductors.