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Besides the chemical constituents, it is the lattice geometry that controlsthe most important material properties. In many interesting compounds, thearrangement of elements leads to pronounced anisotropies, which reflect into avarying degree of quasi two-dimensionality of their low-energy excitations.Here, we start by classifying important families of correlated materialsaccording to a simple measure for the tetragonal anisotropy of their ab initioelectronic (band) structure. Second, we investigate the impact of aprogressively large anisotropy in driving the non-locality of many-bodyeffects. To this end, we tune the Hubbard model from isotropic cubic in threedimensions to the two-dimensional limit and analyze it using the dynamicalvertex approximation. For sufficiently isotropic hoppings, we find theself-energy to be well separable into a static non-local and a dynamical localcontribution. While the latter could potentially be obtained from dynamicalmean-field approaches, we find the former to be non-negligible in all cases.Further, by increasing the model-anisotropy, we quantify the degree of quasitwo-dimensionality which causes this "space-time separation" to break down. Oursystematic analysis improves the general understanding of electroniccorrelations in anisotropic materials, heterostructures and ultra-thin films,and provides useful guidance for future realistic studies.

Anisotropy of electronic correlations: On the applicability of local theories to layered materials