V 2 O 3 is the prototype system for the Mott transition, one of the most fundamental phenomena of electronic correlation. Temperature, doping or pressure induce a metal-to-insulator transition (MIT) between a paramagnetic metal (PM) and a paramagnetic insulator. This or related MITs have a high technological potential, among others, for intelligent windows and field effect transistors. However the spatial scale on which such transitions develop is not known in spite of their importance for research and applications. Here we unveil for the first time the MIT in Cr-doped V 2 O 3 with submicron lateral resolution: with decreasing temperature, microscopic domains become metallic and coexist with an insulating background. This explains why the associated PM phase is actually a poor metal. The phase separation can be associated with a thermodynamic instability near the transition. This instability is reduced by pressure, that promotes a genuine Mott transition to an eventually homogeneous metallic state.

We employ density functional theory plus dynamical mean field theory and identify the physical origin of why two layers of SrVO3 on a SrTiO3 substrate are insulating: the thin film geometry lifts the orbital degeneracy which in turn triggers a Mott-Hubbard transition. Two layers of SrVO3 are just at the verge of a Mott-Hubbard transition and hence ideally suited for technological applications of the Mott-Hubbard transition: the heterostructure is highly sensitive to strain, electric field, and temperature. A gate voltage can also turn the insulator into a metal, so that a transistor with ideal on-off (metal-insulator) switching properties is realized.

In the context of realistic calculations for strongly-correlated materials with d-or f -electrons the efficient computation of multi-orbital models is of paramount importance. Here we introduce a set of invariants for the SU(2)-symmetric Kanamori Hamiltonian which allows to massively speed up the calculation of the fermionic trace in hybridization-expansion continuous-time quantum Monte Carlo algorithms. As an application, we show that, exploiting this set of good quantum numbers, the study of the orbital-selective Mott-transition in systems with up to seven correlated orbitals becomes feasible.

We describe the hybridization-expansion continuous-time quantum Monte Carlo code package "w2dynamics", developed in Wien and Würzburg. We discuss the main features of this multi-orbital quantum impurity solver for the Anderson impurity model, dynamical mean field theory as well as its coupling to density functional theory. The w2dynamics package allows for calculating one-and two-particle quantities; it includes worm and further novel sampling schemes. Details about its download, installation, functioning and the relevant parameters are provided.

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+DMFT against each other and against experiment for SrVO3. We observed a partial compensation of stronger electronic correlations due to the reduced GW bandwidth and weaker correlations due to a larger screening of the RPA interaction, so that the obtained spectra are quite similar and well agree with experiment. Noteworthily, the GW +DMFT better reproduces the position of the lower Hubbard side band.