Computational approaches to correlated electron systems

Abstract

The present thesis is devoted to the theoretical and computational effort toward a better description of strongly correlated electron systems in which strong atomic-like quantum fluctuations give rise to intriguing physical phenomena while simultaneously posing tremendous theoretical challenges. To this end, computational approaches including standard density functionals as well as novel Green's function-based many-body approaches are investigated and applied to real materials and model systems. In Chapter 1, I briefly review the fundamental concepts and theories which are the basic ingredient to the subsequent chapters. In Chapter 2 and 3, I investigate the functional structure of several standard density functional approximations, namely the local density approximation (LDA), generalized gradient approximation (GGA), and the density functional theory plus $U$ (DFT+$U$), in regard to the description of magnetic ground states. Analysis in Chapter 2 clearly clarifies that LDA and GGA have fundamental difference in capturing the magnetic ground state. Furthermore, GGA is shown to intrinsically more favor the magnetic solutions than LDA, which has been observed over many years but never been formally analyzed before. In Chapter 3, I argue that the DFT+$U$ based on charge-only density can provide more reliable and transparent description of the physics rather than the common practice of adopting the spin density functional. This argument is closely related to the conclusion obtained in Chapter 2 in which the fundamental ambiguity is found in adopting the functional form of spin density exchange-correlation energy. A series of applications of DFT+$U$ based on my implementation provided in Chapter 3 clearly corroborate the conclusion. In Chapter 4, I present my application of DFT + dynamical mean-field theory (DMFT) to the recently discovered superconducting infinite-layer nickelate (Nd$_{1-x}$Sr$_x$NiO$_2$). The results obtained from DFT+DMFT exhibit intriguing aspects of this materials which have not been identified by single-particle theories. In Chapter 5, a novel many-body approach, namely the GW + extended dynamical mean-field theory (EDMFT) is introduced. This theory is based on the two fundamental physical quantities: Green's function and screened Coulomb interaction. As a fully diagrammatic approach, this method is free from the known long-standing issues of widely exploited DFT-based approaches, thereby can be a promising candidate for the ab initio electronic structure theory. I elucidate recent application of GW+EDMFT based on my implementation of the method to a three-orbital Hubbard-type model including spatially nonlocal Coulomb interaction. The interplay between Hund's coupling and nonlocal Coulomb interaction is found to play an important role in the Hund's metal physics.