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.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.

arXiv:2505.19852Journal of Physics Condensed MatterJul 15, 20250 citations

Functional Renormalization Group Approach to Correlated Electron Systems

Walter Metzner

AIP conference proceedingsJan 1, 20061 citation

Time-dependent exchange-correlation potential in lieu of self-energy

F. Aryasetiawan

The equation of motion of the Green's function of a many-electron system is shown to be governed by a multiplicative exchange-correlation potential, in contrast to the self-energy. Crucially, this exchange-correlation potential is simply the Coulomb potential of an exchange-correlation hole and fulfills a sum rule. The formulation offers a simple physical interpretation for the propagation of an added electron or hole and may provide a route for density-functional-like approximations for calculating the Green's function.The equation of motion of the Green's function of a many-electron system is shown to be governed by a multiplicative exchange-correlation potential, in contrast to the self-energy. Crucially, this exchange-correlation potential is simply the Coulomb potential of an exchange-correlation hole and fulfills a sum rule. The formulation offers a simple physical interpretation for the propagation of an added electron or hole and may provide a route for density-functional-like approximations for calculating the Green's function.

arXiv:2201.02854Physical review. B./Physical review. BFeb 2, 20227 citations

Theoretical Methods for Strongly Correlated Electrons

David Sénéchal, A.–M. S. Tremblay, C. Bourbonnais

Springer eBooksJan 1, 2004254 citations

CORRELATED ELECTRON SYSTEMS

Victor J. Emery

Aug 1, 1993143 citations

Self-consistency functional equation in strongly correlated electron systems: a different approach

E. I. Grancharova

We propose a new approach to the self-consistency equation, which arises in the problem of the motion of a hole in a quantum antiferromagnet, appropriate to the case of small exchange energy $J$ . The functional equation for the Green function is transformed into a differential equation; its solutions are analyzed and compared to the existing numerical calculations. This method allows one to study the limit of $J\to 0$ . Application to other strongly correlated electron systems is discussed.We propose a new approach to the self-consistency equation, which arises in the problem of the motion of a hole in a quantum antiferromagnet, appropriate to the case of small exchange energy $J$. The functional equation for the Green function is transformed into a differential equation; its solutions are analyzed and compared to the existing numerical calculations. This method allows one to study the limit of $J\to 0$. Application to other strongly correlated electron systems is discussed.

arXiv:cond-mat/0604197Apr 7, 20060 citations

We propose a new approach to the self-consistency equation, which arises in the problem of the motion of a hole in a quantum antiferromagnet, appropriate to the case of small exchange energy

J

. The functional equation for the Green function is transformed into a differential equation; its solutions are analyzed and compared to the existing numerical calculations. This method allows one to study the limit of

J\to 0

. Application to other strongly correlated electron systems is discussed.