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

TL;DR

This paper introduces a simplified approach to the local two-particle vertex in DMFT, enabling efficient inclusion of nonlocal correlations and capturing phenomena like the pseudogap with reduced computational costs.

Contribution

The authors propose a novel simplification of the local full vertex in DMFT and develop two methods to incorporate nonlocal fluctuations efficiently.

Findings

Successfully captures the pseudogap in models

Reduces computational costs significantly

Validates methods against known nonlocal effects

Abstract

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 and confirm that our methods can capture important behaviors such as the pseudo gap in the DMFT + nonlocal calculation. In addition, the numerical costs are largely reduced compared to the conventional methods.