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

Abstract

Besides the chemical constituents, it is the lattice geometry that controls the most important material properties. In many interesting compounds, the arrangement of elements leads to pronounced anisotropies, which reflect into a varying degree of quasi two-dimensionality of their low-energy excitations. Here, we start by classifying important families of correlated materials according to a simple measure for the tetragonal anisotropy of their ab initio electronic (band) structure. Second, we investigate the impact of a progressively large anisotropy in driving the non-locality of many-body effects. To this end, we tune the Hubbard model from isotropic cubic in three dimensions to the two-dimensional limit and analyze it using the dynamical vertex approximation. For sufficiently isotropic hoppings, we find the self-energy to be well separable into a static non-local and a dynamical local contribution. While the latter could potentially be obtained from dynamical mean-field approaches, we find the former to be non-negligible in all cases. Further, by increasing the model-anisotropy, we quantify the degree of quasi two-dimensionality which causes this "space-time separation" to break down. Our systematic analysis improves the general understanding of electronic correlations in anisotropic materials, heterostructures and ultra-thin films, and provides useful guidance for future realistic studies.

12 pages, 7 figures

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• Magnetic phase diagram of the three-dimensional doped Hubbard model
• Zoology of spin and orbital fluctuations in ultrathin oxide films
• Spatial non-locality of electronic correlations beyond GW approximation
• Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
• Confinement-Induced Isosymmetric Metal-Insulator Transition in Ultrathin Epitaxial V2O3 Films