Density-Functional Green Function Theory: Dynamical exchange-correlation field in lieu of self-energy

TL;DR

This paper introduces a novel formalism replacing the self-energy with a dynamical exchange-correlation field, offering a local and potentially more efficient approach to many-electron systems, with applications to model systems and the homogeneous electron gas.

Contribution

It proposes a new formalism using a dynamical exchange-correlation field instead of self-energy, with exact constraints and potential for simplified approximations.

Findings

Applied to model systems like the Hubbard and Anderson models

Studied the exchange-correlation hole in the homogeneous electron gas

Potential for developing local-density approximations

Abstract

The one-particle Green function of a many-electron system is traditionally formulated within the self-energy picture. A different formalism was recently proposed, in which the self-energy is replaced by a dynamical exchange-correlation field, which acts on the Green function locally in both space and time. It was found that there exists a fundamental quantity, referred to as the dynamical exchange-correlation hole, which can be interpreted as effective density fluctuations induced in a many-electron system when a hole or an electron is introduced into the system, as in photoemission and inverse photoemission experiments. The dynamical exchange-correlation potential is simply the Coulomb potential of this exchange-correlation hole, which fulfils a sum rule and an exact constraint, identical to those satisfied by the static exchange-correlation hole in density-functional theory. The proposed formalism has been applied to a number of model systems such as the half-filled one-dimensional Hubbard model, the one-dimensional antiferromagnetic Heisenberg model, and the single-impurity Anderson model. The dynamical exchange-correlation hole and field of the homogeneous electron gas have also been studied with the view of constructing a density-functional approximation such as the local-density approximation. The availability of simple but accurate approximations for the exchange-correlation potential would circumvent costly computations of the traditional self-energy. The formalism may also provide new perspectives and insights into the many-body problem.