In order to gain physical insight into the strongly correlated systems described above, state-of-the-art numerical many body techniques are not only applied but also developed in this research group. One of the big steps forward in the description of strong correlations was the dynamical mean field theory (DMFT), that incorporates all temporal fluctuations. However, if spatial correlations are becoming important (as in the vicinity of second order phase transitions), one has to go one step beyond DMFT. Within the DMFT framework, there are two paths to achieve this inclusion of spatial correlations: its cluster and diagrammatic extensions, respectively. Both are applied and developed further in this research group.
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