Density-functional Green function theory: dynamical exchange-correlation field in lieu of self-energy

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory

Background:

• Traditional one-particle Green function formulation relies on the self-energy picture.
• Computational cost of traditional self-energy calculations can be prohibitive.

Purpose of the Study:

• Introduce a novel formalism for many-electron systems.
• Replace the self-energy with a local dynamical exchange-correlation field.
• Investigate the properties and applications of the dynamical exchange-correlation hole.

Main Methods:

• Developed a new theoretical formalism for the Green function.
• Introduced the concept of the dynamical exchange-correlation hole and potential.
• Applied the formalism to model systems (1D Hubbard, Heisenberg, Anderson models) and homogeneous electron gas.

Main Results:

• The dynamical exchange-correlation potential is derived from the exchange-correlation hole.
• This potential satisfies exact sum rules and constraints, analogous to static DFT.
• Demonstrated applicability to various model systems and the homogeneous electron gas.

Conclusions:

• The new formalism offers a computationally efficient alternative to traditional self-energy methods.
• The dynamical exchange-correlation hole provides new insights into many-body physics.
• Potential for developing accurate density-functional approximations.