Diagrammatic theory for Periodic Anderson Model: Stationary property of the thermodynamic potential

TL;DR

This paper develops a diagrammatic theoretical framework for the Periodic Anderson Model focusing on the stationary property of the thermodynamic potential, applicable to both normal and superconducting states.

Contribution

It introduces a diagrammatic approach considering Coulomb repulsion as a key parameter, establishing the stationary property of the thermodynamic potential with respect to the mass operator.

Findings

Formulated Dyson equations for $c$ and $f$ electrons.

Defined skeleton diagrams for correlation functions and thermodynamic functional.

Proved the stationary property of the renormalized thermodynamic potential.

Abstract

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of $f-$ localized electrons as a main parameter of the theory. $f-$ electrons are strongly correlated and $c-$ conduction electrons are uncorrelated. Correlation function for $f-$ and mass operator for $c-$ electrons are determined. The Dyson equation for $c-$ and Dyson-type equation for $f-$ electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential about the variation of the mass operator is established. The result is appropriate as for normal and as for superconducting state of the system.