Simplification of the Local Full Vertex in the Impurity Problem in DMFT and Its Applications for the Nonlocal Correlation

The two-particle vertex function is crucial for the diagrammatic extensions beyond DMFT for the nonlocal fluctuation. However, estimating the two-particle quantities is still a challenging task. In this study, we propose a simplification of the local two-particle full vertex and, using the simplified full vertex, we develop two methods to take into account the nonlocal fluctuation. We apply these methods to several models to validate them. Although some quantitative improvements are required, our methods can capture important behaviors such as the pseudo gap in the DMFT + nonlocal calculation with much lower numerical costs compared to the conventional methods.