Extended Dynamical Mean Field Theory and GW method

TL;DR

This paper advances the extended dynamical mean field theory (E-DMFT) by providing a new derivation, implementation, and integration with GW methods, enabling more accurate modeling of correlated electron systems and phase transitions.

Contribution

It introduces an intuitive derivation, a real Hubbard-Stratonovich implementation, and combines E-DMFT with GW to improve treatment of non-local interactions and response functions.

Findings

Phase diagram of 3D U-V model obtained

E-DMFT+GW results align better with DMRG

Method to incorporate momentum dependence in response functions

Abstract

We develop the extended dynamical mean field theory (E-DMFT) with a view towards realistic applications. {\bf 1)} We introduce an intuitive derivation of the E-DMFT formalism. By identifying the Hartree contributions before the E-DMFT treatment, it allows to handle systems in symmetry breaking phases within a simple formalism. {\bf 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. {\bf 3)} We present a formalism incorporating E-DMFT with Cellular DMFT. {\bf 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. {\bf 5)} In order to handle the generic Coulomb repulsion within E-DMFT, we describe a method to tailor E-DMFT so that proper momentum dependence can be kept in general response functions.