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The two-particle vertex function is crucial for the diagrammatic extensionsbeyond DMFT for the nonlocal fluctuation. However, estimating the two-particlequantities is still a challenging task. In this study, we propose asimplification of the local two-particle full vertex and, using the simplifiedfull vertex, we develop two methods to take into account the nonlocalfluctuation. We apply these methods to several models and confirm that ourmethods can capture important behaviors such as the pseudo gap in the DMFT +nonlocal calculation. In addition, the numerical costs are largely reducedcompared to the conventional methods.

Simplification of the local full vertex in the impurity problem in DMFT and its applications for the nonlocal correlation