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While second-order phase transitions always cause strong non-localfluctuations, their effect on spectral properties crucially depends on thedimensionality. For the important case of three dimensions, we show that theelectron self-energy is well separable into a local dynamical part and staticnon-local contributions. In particular, our non-perturbative many-bodycalculations for the 3D Hubbard model at different fillings demonstrate thatthe quasi-particle weight remains essentially momentum-independent, also in thepresence of overall large non-local corrections to the self-energy. Relying onthis insight we propose a "space-time-separated" scheme for many-bodyperturbation theory that is up to ten times more efficient than currentimplementations. Besides these far-reaching implications for state-of-the-artelectronic structure schemes, our analysis will also provide guidance to thequest of going beyond them.

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