Dynamical Mean Field Theory and Electronic Structure Calculations

TL;DR

This paper develops a continuum formulation of dynamical mean field theory (DMFT), establishing a unique functional for local Green's functions and proposing approximations for strong coupling regimes using quantum impurity models.

Contribution

It introduces a continuum-based formulation of DMFT with a unique functional for local Green's functions and diagrammatic rules for perturbative calculations.

Findings

Established existence of a unique functional for local Green's functions.

Presented diagrammatic rules for perturbative calculations.

Proposed approximations for strong coupling using quantum impurity models.

Abstract

We formulate the dynamical mean field theory directly in the continuum. For a given definition of the local Green's function, we show the existence of a unique functional, whose stationary point gives the physical local Green's function of the solid. We present the diagrammatic rules to calculate it perturbatively in the interaction. Inspired by the success of dynamical mean field calculations for model Hamiltonian systems, we present approximations to the exact saddle point equations which may be used in the strong coupling regime, by using mappings onto generalized quantum impurity models.