# On the duality of ring and ladder diagrams and its importance for many-electron perturbation theories

## TL;DR

This paper reveals the duality of ring and ladder diagrams in many-electron perturbation theories, showing how their understanding can improve computational efficiency and accuracy in electronic structure calculations.

## Contribution

It introduces a diagrammatic decomposition highlighting the duality of ring and ladder diagrams and demonstrates an effective approximation for ladder diagrams using second-order perturbation theory.

## Key findings

- Ladder diagrams can be approximated by second-order perturbation theory.
- The approach reduces coupled cluster calculation costs by two orders of magnitude.
- The approximation maintains accuracy in electronic correlation energy calculations.

## Abstract

We present a diagrammatic decomposition of the transition pair correlation function for the uniform electron gas. We demonstrate explicitly that ring and ladder diagrams are dual counterparts that capture significant long- and short-ranged interelectronic correlation effects, respectively. Our findings help to guide the further development of approximate many-electron theories and reveal that the contribution of the ladder diagrams to the electronic correlation energy can be approximated in an effective manner using second-order perturbation theory. We employ the latter approximation to reduce the computational cost of coupled cluster theory calculations for insulators and semiconductors by two orders of magnitude without compromising accuracy.