Improvement of the simplification method for the local two-particle full-vertex towards precise frequency behavior

Estimating the local two-particle vertex functions, which are crucial for capturing the spatial fluctuation of the effective field beyond the single-site DMFT, is still challenging. In our previous work, we developed a computationally efficient method for estimating the local full-vertex in DMFT, where we can obtain the local two-particle full-vertex from the one-particle self-energy. In this study, we further enhance our method by refining its formulation to be more faithful to the diagrammatic structure of the full-vertex. With this improvement, we can qualitatively reproduce the characteristic frequency structures of the full-vertex obtained by the numerically exact methods. In particular, the improved version of the simplified full-vertex captures a sharp value change in the cross structure.