Justifying quasiparticle self-consistent schemes via gradient optimization in Baym-Kadanoff theory.

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Theory
• Computational Materials Science

Background:

• Determining the best non-interacting Green's function for interacting many-body electronic systems is crucial for realistic material property descriptions.
• Baym-Kadanoff theory offers a framework to find ground-state properties by minimizing a total energy functional of the one-particle Green's function.

Purpose of the Study:

• To investigate which non-interacting Green's function best approximates an interacting many-body electronic system.
• To provide a theoretical justification for the quasiparticle self-consistent GW (QSGW) method in electronic structure calculations.

Main Methods:

• Utilizing the Baym-Kadanoff theory and the Klein functional.
• Minimizing the length of the gradient of the total energy functional with respect to non-interacting Green's functions.
• Analyzing the self-consistent Dyson equation and quasiparticle properties.

Main Results:

• Minimizing the gradient length yields self-consistent equations identical to the QSGW approach.
• This result is general and applicable to any self-energy operator, not limited to the GW approximation.
• In cases of multiple quasiparticle solutions, minimizing the gradient selects the solution with the largest quasiparticle weight.

Conclusions:

• The study provides an a priori justification for the QSGW method in electronic structure calculations.
• It highlights the primary importance of the diagonal part of the Dyson equation in the quasiparticle basis.
• The findings offer a principled way to select the most appropriate quasiparticle solution.