Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and many-body methods is particularly promising. A crucial role is also played by a systematic method for deriving a low-energy model, which bridges the gap between real and model systems. In this article, an overview is given tracing the development from the LDA+U to the latest progress in combining the G W method and (extended) dynamical mean-field theory ( G W +EDMFT). The emphasis is on conceptual and theoretical aspects rather than technical ones.
We review the basic ideas of the dynamical mean field theory (DMFT) and some of the insights into the electronic structure of strongly correlated electrons obtained by this method in the context of model Hamiltonians. We then discuss the perspectives for carrying out more realistic DMFT studies of strongly correlated electron systems and we compare it with existent methods, LDA and LDA+U. We stress the existence of new functionals for electronic structure calculations which allow us to treat situations where the single--particle description breaks down such as the vicinity of the Mott transition.
We propose a dynamical mean-field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean-field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional "LDA+DMFT," such as Hubbard interaction parameters and double-counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.
Computational chemistry has made remarkable progress in the last couple of decades due to the availability of better and more powerful computers. However, there is definitely more room for improvement. There are problems in material science and biology that require 102 to 104 atoms to be considered and the importance of such systems cannot be over-emphasized. Addressing such systems with ab-initio methods is still a quantum chemist’s dream. ¨ Brute force solutions of the Schrodinger equation are not possible for reasonably interesting and important systems due to the large number of Slater determinants that have to be stored in a computer’s memory. Thus electronic structure theorists have made chemically and mathematically intuitive approximations to simplify the problems. A particularly difficult class of systems that is very interesting to the theoretical and experimental chemists is the strongly correlated systems. High Tc superconductors, nanotubes, graphene sheets, transition metal complexes and photosynthetic materials all fall under this category. These systems are too large to be treated by traditional quantum chemical methods. Another reason why such systems have not been studied sufficiently by ab-initio method is that they comprise of complicated strong electron-electron correlation (and therefore the name strongly correlated), thus, making them impossible to be qualitatively defined by a molecular orbital picture, which has been a quantum chemist’s fa- vorite tool for a long time now. Therefore, in this thesis, we have tried to develop, improve and apply methods for treating such strongly correlated systems. The thesis is broadly divided into two parts. In the first part, we discuss the orbital optimized DMRG method developed to treat static correlation in large strongly correlated systems. In the next part we discuss the two methods that can treat dynamic correlation in such complicated systems.
The study of strongly correlated materials remains one of the most challenging and active frontiers in condensed matter physics. In these systems, the intricate interplay between electrons' kinetic energy and their mutual Coulomb repulsion gives rise to a plethora of exotic phenomena, from high-temperature superconductivity to giant magnetoresistance, which cannot be explained by conventional one-electron theories. This necessitates the development and application of advanced theoretical and computational methods capable of capturing the essential physics of strong electronic correlations. A diverse array of numerical and analytical techniques has been developed to tackle the many-body problem. However, no single method serves as a panacea; each comes with its own set of strengths and weaknesses, and their domains of applicability vary significantly. The choice of an appropriate approximation is therefore highly dependent on the specific physical system and the scientific question at hand. Different problems may benefit from different, and sometimes complementary, methodological perspectives. This thesis focuses primarily on the application and development of local or quasi-local approaches. The rationale for this focus is rooted in the physical reality of many key correlated materials, such as transition metal oxides, heavy-fermion systems or molecular solids like alkali-doped fullerenes, where the local on-site electronic interaction is the dominant energy scale. By prioritizing the accurate treatment of local physics, these methods provide a robust and computationally efficient approximation for understanding a wide range of material properties. Recent experimental and theoretical advancements—spanning the rich physics of multiorbital compounds, the precise control over interactions in ultracold atomic gases, and the complex interplay in electron-phonon coupled systems—have created an urgent need for theoretical frameworks that can deliver reliable and rapid insights. The methods explored in this work are meant to address these challenges, offering a balance between accuracy and computational feasibility. Given the variety of topics addressed, from methodological developments to their application in diverse physical contexts, this thesis will try to be as detailed and self-contained as necessary, providing a clear exposition of the underlying concepts and technical aspects.