Ab-initio Approaches to Correlated Materials

In this chapter, we introduce and briefly review the theoretical background and computational methods that have been used throughout the subsequent chapters. Ab-initio is Latin for “from the beginning”, which captures perfectly our intentions for the theoretical framework we would like to have. Ideally, we could write down a solvable quantum mechanical theory that builds up from the basic interactions between electrons and ions that can predict and describe properties of solids. Thus, approximations are required to study real materials. We review the following techniques: density-functional theory (DFT) (with an emphasis on all-electron, full potential codes) and beyond DFT methods including DFT+U and DFT + dynamical mean-field theory (DMFT). Finally, we discuss the implementation of DFT+DMFT in a popular DFT code, WIEN2k interfaced with a many-body physics library, TRIQS.