On the separability of dynamical and non-local correlations in three dimensions

TL;DR

This paper demonstrates that in three-dimensional systems, the electron self-energy can be effectively separated into local dynamical and static non-local parts, enabling more efficient computational methods.

Contribution

It introduces a space-time-separated scheme for many-body perturbation theory based on the separability of correlations in 3D systems, improving efficiency significantly.

Findings

Self-energy in 3D is well separable into local and non-local parts.

Quasi-particle weight remains momentum-independent despite non-local corrections.

Proposed scheme is up to ten times more efficient than existing methods.

Abstract

While second-order phase transitions always cause strong non-local fluctuations, their effect on spectral properties crucially depends on the dimensionality. For the important case of three dimensions, we show that the electron self-energy is well separable into a local dynamical part and static non-local contributions. In particular, our non-perturbative many-body calculations for the 3D Hubbard model at different fillings demonstrate that the quasi-particle weight remains essentially momentum-independent, also in the presence of overall large non-local corrections to the self-energy. Relying on this insight we propose a "space-time-separated" scheme for many-body perturbation theory that is up to ten times more efficient than current implementations. Besides these far-reaching implications for state-of-the-art electronic structure schemes, our analysis will also provide guidance to the quest of going beyond them.