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Materials with correlated electrons often respond very strongly to external or internal influences, leading to instabilities and states of matter with broken symmetry. This behavior can be studied theoretically either by evaluating the linear response characteristics, or by simulating the ordered phases of the materials under investigation. We developed the necessary tools within the dynamical mean-field theory (DMFT) to search for electronic instabilities in materials close to spin-state crossovers and to analyze the properties of the corresponding ordered states. This investigation, motivated by the physics of LaCoO$_3$, led to a discovery of condensation of spinful excitons in the two-orbital Hubbard model with a surprisingly rich phase diagram. The results are reviewed in the first part of the article. Electronic correlations can also be the driving force behind structural transformations of materials. To be able to investigate correlation-induced phase instabilities we developed and implemented a formalism for the computation of total energies and forces within a fully charge self-consistent combination of density functional theory and DMFT. Applications of this scheme to the study of structural instabilities of selected correlated electron materials such as Fe and FeSe are reviewed in the second part of the paper.
We implemented the derivative of the free energy functional with respect to the atom displacements, so called force, within the combination of Density Functional Theory and the Embedded Dynamical Mean Field Theory. We show that in combination with th
The new challenges posed by the need of finding strong rare-earth free magnets demand methods that can predict magnetization and magnetocrystalline anisotropy energy (MAE). We argue that correlated electron effects, which are normally underestimated
We discuss the recently proposed LDA+DMFT approach providing consistent parameter free treatment of the so called double counting problem arising within the LDA+DMFT hybrid computational method for realistic strongly correlated materials. In this app
We present an ab initio quantum theory of the finite temperature magnetism of iron and nickel. A recently developed technique which combines dynamical mean-field theory with realistic electronic structure methods, successfully describes the many-body
We have implemented the $GW$+dynamical mean field theory (DMFT) approach in the Vienna ab initio simulation package. Employing the interaction values obtained from the locally unscreened random phase approximation (RPA), we compare $GW$+DMFT and LDA+