Diagram theory for the periodic anderson model: Stationarity of the thermodynamic potential

Abstract

We develop a diagram theory for the periodic Anderson model assuming that the Coulomb repulsion of localized f electrons is the main parameter of the theory. The f electrons are strongly correlated and the c conduction electrons are uncorrelated. We determine the f -electron correlation function and the c-electron mass operator. We formulate the Dyson equation for c electrons and a Dyson-type equation for f electrons and their propagators. We define the skeleton diagrams for the correlation function and the thermodynamic functional. We establish the stationarity of the renormalized thermodynamic potential under variation of the mass operator. The obtained results are applicable to both the normal and the superconducting system states.

Stationary property of the thermodynamic potential of the Hubbard model in strong coupling diagrammatic approach for superconducting state

“…3 of paper [18], obtained for Λ functional of PAM topologically coincide with the skeleton diagrams of our Fig. 2 for the same functional, but of quite a different model.…”

“…From comparison of the results obtained for the PAM (see paper [18]) and the results of the present paper for the HM the topological coincidence of the diagrams for both models has been revealed.…”

“…For example, comparison of the skeleton diagrams of Fig. 10 of paper [18] with the diagrams of Fig. 4 of the present paper reveals the full coincidence upon replacement of the Green's functions c G by T .…”

“…The new diagram technique for such strongly correlated systems has been developed in our earlier papers [8][9][10][11][12][13][14][15][16][17][18]. This diagram technique uses the algebra of Fermi operators and relies on the generalized Wick theorem which contains, apart from usual Feynman contributions, additional irreducible structures.…”

“…Using the definition (18) of the mass operator ˆλ Σ we can rewrite the functional 1 ( ) Y λ in the form…”