Extended dynamical mean-field theory and GW method

We develop the extended dynamical mean field theory (E-DMFT) with a view towards realistic applications. 1) We introduce an intuitive derivation of the E-DMFT formalism. By identifying the Hartree contributions before the EDMFT treatment, it allows to handle systems in symmetry breaking phases within a simple formalism. 2) We make a new implementation of E-DMFT through real Hubbard-Stratonovich transformation to decouple the non-local two-particle interactions. We apply it to a 3D U-V model and investigate the behavior of the various Green’s functions, especially the density susceptibility, as the density instability is approached. We obtain the phase diagram at a finite temperature. 3) We present a formalism incorporating E-DMFT with Cellular DMFT. 4) We suggest an improvement of the E-DMFT approach by combining it with a generalized GW method. The method combines the local self-energy from E-DMFT and the non-local ones from the perturbative calculation of GW. We apply the method to a 1D U-V model with two sublattices carrying different chemical potentials. By comparing with those from DMRG, we show the results are shifted in the correct direction due to the GW contributions. 5) In order to handle the generic Coulomb repulsion within E-DMFT, we describe a method to tailor E-DMFT so that proper momentum