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The Multi-Tier GW+EDMFT Scheme

F. Aryasetiawan, Fredrik Nilsson

Published Aug 3, 2022• 0 citations
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Abstract

In Chap. 7 the multitier downfolding scheme was introduced from a general perspective, and in Chap. 8 the combination of GWA (Chap. 4) with extended dynamical-mean field theory (Chap. 5), the so called GW+EDMFT method, was described. In this chapter the multitier scheme applied to GW+EDMFT will be discussed. For completeness we will begin by reintroducing the multitier machinery applied specifically to GW+EDMFT and then we review the most important results.

DOI
10.1063/9780735422490_009

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In Chap. 7 the multitier downfolding scheme was introduced from a general perspective, and in Chap. 8 the combination of GWA (Chap. 4) with extended dynamical-mean field theory (Chap. 5), the so called GW+EDMFT method, was described. In this chapter the multitier scheme applied to GW+EDMFT will be discussed. For completeness we will begin by reintroducing the multitier machinery applied specifically to GW+EDMFT and then we review the most important results.
We explore the combination of the extended dynamical mean field theory (EDMFT) with the GW approximation (GWA); the former sums the local contributions to the self-energies to infinite order in closed form and the latter handles the nonlocal ones to lowest order. We investigate the different levels of self-consistency that can be implemented within this method by comparing to the exact quantum Monte Carlo solution of a finite-size model Hamiltonian. We find that using the EDMFT solution for the local self-energies as input to the GWA for the nonlocal self-energies gives the best result.
Extended dynamical mean-field theory (EDMFT) is insufficient to describe non-local effects in strongly correlated systems, since corrections to the mean-field solution are generally large. We present an efficient scheme for the construction of diagrammatic extensions of EDMFT that avoids usual double counting problem by using an exact change of variables (the dual boson formalism) to distinguish the correlations included in the mean-field solution and those beyond. With a computational efficiency comparable to EDMFT+GW approach, our scheme significantly improves on the charge order transition phase boundary in the extended Hubbard model.