Examining phase stabilities and phase equilibria in strongly correlated materials asks for a next level in the many-body extensions to the local-density approximation (LDA) beyond mainly spectroscopic assessments. Here we put the charge self-consistent LDA+dynamical mean-field theory (DMFT) methodology based on projected local orbitals for the LDA+DMFT interface and a tailored pseudopotential framework into action in order to address such thermodynamics of realistic strongly correlated systems. Namely a case study for the electronic phase diagram of the well-known prototype Mott-phenomena system V2O3 at higher temperatures is presented. We are able to describe the first-order metal-to-insulator transitions with negative pressure and temperature from the self-consistent computation of the correlated total energy in line with experimental findings.

We shed light on the interplay between structure and many-body effects relevant for itinerant ferromagnetism in LaAlO3/SrTiO3 heterostructures. The realistic correlated electronic structure is studied by means of the (spin-polarized) charge self-consistent combination of density functional theory (DFT) with dynamical mean-field theory (DMFT) beyond the realm of static correlation effects. Though many-body behavior is also active in the defect-free interface, a ferromagnetic instability occurs only with oxygen vacancies. A minimal Ti two-orbital eg-t2g description for the correlated subspace is derived. Magnetic order affected by quantum fluctuations builds up from effective double exchange between modified nearly-localized eg and mobile xy electrons.

The interplay of spin-orbit coupling and strong electronic correlations is studied for the single-layer and the bilayer compound of the strontium ruthenate Ruddlesden-Popper series by a combination of first-principles band-structure theory with mean-field rotationally invariant slave bosons. At equilibrium strongly renormalized (spin-orbit-split) quasiparticle bands are traced and a thorough description of the low-energy regime for the nearly ferromagnetic bilayer system in accordance with experimental data is presented. The metamagnetic response of Sr 3 Ru 2 O 7 in finite magnetic field H is verified and a detailed analysis of the underlying correlated electronic structure provided. Intriguing multiorbital physics on both local and itinerant level, such as competing paramagnetic and diamagnetic contributions, is observed with important differences depending on the magneticfield angle θ with the crystallographic c axis.

The combination of the local-density approximation (LDA) with the rotationally invariant slave-boson theory (RISB) is used to investigate the realistic correlated electronic structure of Sr 3 Ru 2 O 7 . From Wannier-downfolding the low-energy band structure to a three-band model for the Ru(t 2g ) states, the interacting problem is solved including intra-and inter-orbital Hubbard terms as well as spin-flip and pair-hopping interactions. Therewith it is possible to obtain valuable insight into the orbital occupations, relevant local spin multiplets, and the fermiology with increasing correlation strength. Besides generic correlation-induced band-narrowing and -shifting, an intriguing quasiparticle structure close to the Fermi level is found in the neighborhood of the notorious g 2 pocket in the Brillouin zone. Along the G-X direction in k-space, that structure appears very sensitive to electronic self-energy effects. The subtle sensitivity, connected also to its manifest multi-orbital character, may put this very low-energy structure in context with the puzzling metamagnetic properties of the compound.

The theory of correlated electron systems on a lattice proves notoriously complicated because of the exponential growth of Hilbert space. Mean-field approaches provide valuable insight when the self-energy has a dominant local structure. Additionally, the extraction of effective low-energy theories from the generalized many-body representation is highly desirable. In this respect, the rotational-invariant slave boson (RISB) approach in its mean-field formulation enables versatile access to correlated lattice problems. However in its original form, due to numerical complexity, the RISB approach is limited to about three correlated orbitals per lattice site. We thus present a thorough symmetry-adapted advancement of RISB theory, suited to efficiently deal with multi-orbital Hubbard Hamiltonians for complete atomic-shell manifolds. It is utilized to study the intriguing problem of Hund's physics for three-and especially five-orbital manifolds on the correlated lattice, including crystal-field terms as well as spin-orbit interaction. The well-known Janus-face phenomenology, i.e. strenghtening of correlations at smaller-to-intermediate Hubbard U accompanied by a shift of the Mott transition to a larger U value, has a stronger signature and more involved multiplet resolution for five-orbital problems. Spin-orbit interaction effectively reduces the critical local interaction strength and weakens the Janus-face behavior. Application to the realistic challenge of Fe chalcogenides underlines the subtle interplay of the orbital degrees of freedom in these materials. U J H /U = 0.0 J H /U = 0.1 J H /U = 0.2 J H /U = 0.3 J H /U = 0.4 J H /U = 0.7 U J H /U = 0.0 J H /U = 0.1 J H /U = 0.2 J H /U = 0.3 J H /U = 0.4 J H /U = 0.7