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

TL;DR

This paper improves a computational method for estimating local two-particle vertex functions in DMFT, enabling more accurate frequency behavior representation and capturing characteristic structures with better fidelity.

Contribution

The authors refine their previous method to better reflect the diagrammatic structure of the full-vertex, enhancing the accuracy of frequency behavior modeling.

Findings

Qualitative reproduction of characteristic frequency structures.

Capture of sharp value changes in the cross structure.

Enhanced fidelity to the diagrammatic structure.

Abstract

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.