Methodological study of computational approaches to address the problem of strong correlations
Creators: name: Lee, Juho
Publisher: name: No Publisher Supplied
Year: 2017

description: The main focus of this thesis is the detailed investigation of computational methods to tackle strongly correlated materials in which a rich variety of exotic phenomena are found.    A many-body problem with sizable electronic correlations can no longer be explained by independent-particle approximations such as density functional theory (DFT) or tight-binding approaches. The influence of an electron to the others is too strong for each electron to be treated as an independent quasiparticle and consequently those standard band-structure methods fail even at a qualitative level.    One of the most powerful approaches for strong correlations is the dynamical mean-field theory (DMFT), which has enlightened the understanding of the Mott transition based on the Hubbard model. For realistic applications, the dynamical mean-field theory is combined with various independent-particles approaches. The most widely used one is the DMFT combined with the DFT in the local density approximation (LDA), so-called LDA+DMFT. In this approach, the electrons in the weakly correlated orbitals are calculated by LDA while others in the strongly correlated orbitals are treated by DMFT.  Recently, the method combining DMFT with Hedin's $GW$ approximation was also developed, in which the momentum-dependent self-energy is also added.    In this thesis, we discuss the application of those methodologies based on DMFT. First, we apply the dynamical mean-field theory to solve the 3-dimensional Hubbard model in Chap. 3.  In this application, we model the interface between the thermodynamically coexisting metal and Mott insulator. We show how to model the required slab geometry and extract the electronic spectra. We construct an effective Landau free energy and compute the variation of its parameters across the phase diagram. Finally, using a linear mixture of the density and double-occupancy, we identify a natural Ising order parameter which unifies the treatment of the bandwidth and filling controlled Mott transitions.    Secondly, we study the double-counting problem, a subtle issue that arises in LDA+DMFT.  We propose a highly precise double-counting functional, in which   the intersection of LDA and DMFT is calculated exactly, and implement   a parameter-free version of the LDA+DMFT that is tested on  one of the simplest strongly correlated systems, the H2 molecule. We show that the exact double-counting treatment along with a good DMFT projector leads to very accurate and total energy and excitation spectrum of H$_2$ molecule.    Finally, we implement various versions of $GW$+DMFT, in its fully self-consistent way, one shot GW  approximation, and quasiparticle self-consistent scheme, and studied how well these combined methods  perform on H$_2$ molecule as compared to more established methods such as LDA+DMFT.   We found that most flavors of GW+DMFT break down in strongly correlated regime due to causality  violation. Among GW+DMFT methods, only the self-consistent quasiparticle GW+DMFT with  static double-counting, and a new method with causal double-counting, correctly recover the atomic  limit at large H-atom separation. While some flavors of GW+DMFT improve the single-electron  spectra of LDA+DMFT, the total energy is best predicted by LDA+DMFT, for which the exact  double-counting is known, and is static.