# Unifying first-principles and model approaches for strongly correlated materials : Interplay between long- and short-range correlations

Sammanfattning: In materials with open 3$d$ and 4$f$ shells the valence electrons are relatively localized around the atoms which leads to large electron-electron correlations. These, so called strongly correlated materials, exhibit many intriguing properties such as high $T_c$ superconductivity, colossal magneto-resistance and heavy fermion behaviour. The strong electron-electron correlations make these materials extremely difficult to describe theoretically since mean-field and perturbative treatments break down. In so called LDA+dynamical mean-field theory (LDA+DMFT) the strong local correlations are treated to all orders but the nonlocal correlations are omitted. In this thesis we use and develop methods that can treat both the long-range and strong local correlations from first principles. We show that a proper treatment of the long-range correlations is essential to get a correct description of the satellite features in the spectral function for a number of transition metal compounds. We also investigate and analyse trends in the effective Coulomb interaction for lanthanide and cuprate compounds. The first part of the thesis provides an introduction to the theory as well as a discussion of the most important results and conclusions and the second part consists of the papers. In Paper I and VI we compute and analyse the effective Coulomb interaction for a number of lanthanides and cuprates using the constrained random-phase approximation (cRPA). In Paper II we compute the spectral function of La$_2$CuO$_4$, the parent compound of the cuprate high $T_c$ superconductor, using LDA+DMFT with a dynamical effective Coulomb interaction calculated with the cRPA. In Paper III-IV we develop a multitier combination of $GW$ and DMFT and apply it to the cubic peroviskites SrVO$_3$ and SrMoO$_3$ as well as stretched sodium and Paper V is a review of first-principle methods for computing the electronic structure of correlated materials.

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