Tiling with triangles: parquet and $GW\gamma$ methods unified

TL;DR

This paper unifies the parquet formalism and $GW\gamma$ approach into a single vertex correction theory, highlighting advantages like rapid decay of vertex functions and scale separation, improving computational efficiency.

Contribution

It introduces a unified framework for parquet and $GW\gamma$ methods, enabling more efficient calculations by exploiting scale separation and decay properties.

Findings

Vertex functions decay quickly with frequency and distance.

The unified method maintains accuracy without drawbacks of previous solvers.

Scale separation improves computational efficiency.

Abstract

The parquet formalism and Hedin's $GW\gamma$ approach are unified into a single theory of vertex corrections, corresponding to an exact reformulation of the parquet equations in terms of boson exchange. The method has no drawbacks compared to previous parquet solvers but has the significant advantage that the vertex functions decay quickly with frequencies and with respect to distances in real space. These properties coincide with the respective separation of the length and energy scales of the two-particle correlations into long/short-ranged and high/low-energetic.