Correlated electrons in transition metal oxides: From configuration-interaction to cluster DMFT calculations

Condensed matter physics is dedicated to understanding the collective behavior of large numbers of particles and the properties of matter in various condensed phases. Theoretical physicists have developed a variety of approximation methods and sophisticated models to tackle the complexities of these many-body systems thereby providing insights into the origins of the exotic phenomena observed in experiments and unraveling the underlying microscopic mechanisms. Strongly correlated electron systems, where electron-electron interactions play a dominant role and cannot be explained by effective one-particle theory, have given rise to a variety of fascinating phenomena that continue to challenge and expand our understanding of condensed matter physics. Transition metal oxides serve as ideal platforms for studying strong correlations due to the localized nature of d-orbitals and the complex interplay between charge, spin, and orbital degrees of freedom. This thesis explores various levels of approximation methods, including cluster calculations using configuration interaction in static mean fields (CI+MF), density functional theory (DFT), dynamical mean-field theory (DMFT), cluster dynamical mean-field theory (cDMFT) and density functional theory+dynamical mean-field theory with charge self-consistency loop (DFT+DMFT csc). Beyond the scope of approximation techniques, this study also addresses the influence of structural distortions and carefully examines which orbitals need to be included explicitly in the low-energy effective model to better capture the essential physics of each system. The investigation centers on d-orbital materials—specifically ruthenates, cuprates, and nickelates—as model systems to probe the effectiveness and limitations of each approximation method. By comparing simulation results with experimental data on both single-particle observables (effective mass, spectral function) and two-particle observables (spin susceptibility), we aim to assess the accuracy and applicability of each theoretical approach in describing these complex materials.