Solving the Low-Energy Model

Abstract

In this chapter we will investigate how the downfolding techniques developed in the previous chapter can be used to investigate strongly correlated materials in practice. In Chapter 5, we discussed dynamical mean-field theory (DMFT) in detail. DMFT is a method that can be used to solve the Hubbard Hamiltonian, usually under the assumption that the self-energy only has onsite components. Off-site components of the self-energy can be included by extension to cluster DMFT, however it is computationally costly. The GW+DMFT method extends this approach by accounting for the long-range self-energy using the GWA. The main focus of the chapter is to discuss how DMFT can be used to perform calculations for real materials, both by combining it with density functional theory (DFT) and the one-shot GWA. However, we will begin by discussing the widely used DFT+U method where a Hubbard $U$ term is added to the DFT total energy functional.