Total Energy beyond GW: Exact Results and Guidelines for Approximations

Area of Science:

• Quantum Chemistry
• Condensed Matter Physics
• Computational Many-Body Physics

Background:

• Accurate calculation of total energy and electron spectra is crucial in many-body physics.
• The one-body Green's function (GF) theoretically provides exact results but requires approximations in practice.
• Approximate self-energies are commonly used, leading to inaccuracies.

Purpose of the Study:

• To derive expressions for exact exchange-correlation energy contributions from approximate self-energies.
• To establish a consistent framework for calculating electronic properties.
• To demonstrate the importance of ingredient consistency in many-body perturbation theory.

Main Methods:

• Derivation of new expressions within many-body perturbation theory.
• Utilizing response functions and insights from time-dependent density functional theory.
• Testing the approach on the exactly solvable symmetric Hubbard dimer model.

Main Results:

• Expressions yielding exact exchange-correlation energy for any interaction strength were derived.
• Consistency in combining theoretical ingredients was identified as key for accuracy.
• The method's validity was confirmed using the Hubbard dimer model.

Conclusions:

• Consistent application of theoretical ingredients is essential for accurate Green's function calculations.
• This framework allows for exact exchange-correlation energy contributions even with approximate self-energies.
• The findings offer a pathway to more reliable electronic structure calculations.