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 dynamical mean field theory (DMFT), is still challenging. In our previous work [R. Mizuno et al., J. Phys. Soc. Jpn. 91, 034002 (2022)], 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.