Separability of dynamical and nonlocal correlations in three dimensions

While second-order phase transitions always cause strong nonlocal 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 nonlocal contributions. In particular, our nonperturbative many-body calculations for the three-dimensional Hubbard model at different fillings demonstrate that the quasiparticle weight remains essentially momentum independent, including in the presence of overall large nonlocal 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.