| Strongly-correlated materials are a rich playground for physical phenomena, exhibiting complex phase diagrams with many competing orders. Ab initio insights into materials combined with physical ideas provide the ability to identify the organizing principles driving the correlated electronic behavior and pursue first-principles design of new compounds. Realistic modeling of correlated materials is an active area of research, especially with the recent merger of density functional theory (DFT) with dynamical mean-field theory (DMFT).;This thesis is structured in two parts. The first describes the methods and algorithmic developments which drive advances in DFT+DMFT. In Ch. 2 and 3, we provide an overview of the two foundational theories, DMFT and DFT. In the second half of Ch. 3, we describe some of the principles guiding the combination of the two theories to form DFT+DMFT. In Ch. 4, we describe the algorithm lying at the heart of modern DFT+DMFT implementations, the hybridization expansion formulation of continuous-time quantum monte carlo (CTQMC) for the general Anderson impurity problem, as well as a fast rejection algorithm for speeding-up the local trace evaluation. The final chapter in the methods section describes an algorithm for direct sampling of the partition function, and thus the free energy and entropy, of simple Anderson impurity models within CTQMC.;The second part of the thesis is a collection of applications of our ab initio approach to key correlated materials. We first apply our method to plutonium binary alloys (Ch. 6), which when supplemented with slave-boson mean-field theory, allows us to understand the observed photoemission spectra. Ch. 7 describes the computation of spectra and optical conductivity for rare-earth nickelates grown as epitaxial thin films. In the final two chapters, we turn our attention to the high-temperature superconductors. In the first, we show that the charge-transfer energy is a key chemical variable which controls the superconducting transition temperatures across the cuprate families. In the second, we extend this idea towards first-principles design of cuprates by exploring a new family of copper oxysulfides. |
