Diagrammatic theory for the Anderson impurity model: Stationary property of the thermodynamic potential

Abstract

We propose a diagrammatic theory around the atomic limit for the normal state of the Anderson impurity model. The new diagram method is based on Wick's theorem for conduction electrons and a generalized Wick's theorem for strongly correlated impurity electrons, which coincides with the definition of the Kubo cumulant. We prove a linked-cluster theorem for the mean of the evolution operator and obtain Dysontype equations for the one-particle propagators. The main element in these equations is the impurity electron correlation function, which contains the spin, charge, and pairing fluctuations of the system. We express the system thermodynamic potential in terms of the full propagator of conduction electrons and the correlation function. We establish that the thermodynamic potential is stationary under changes of the correlation function.

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Diagrammatic analysis of the Hubbard model: Stationary property of the thermodynamic potential

“…The strong coupling diagram theory used by us needs new conceptions and new equations and they are used to prove stationary property of thermodynamic potential for strongly correlated systems. Such a proof has been already achieved for Anderson impurity model in paper [16] .…”

Diagram theory for the twofold-degenerate Anderson impurity model

“…We use the perturbation theory elaborated previously for strongly correlated electron systems both of non degenerate [5][6][7][8][9][11][12][13][14] and of degenerate forms [10]. We study the process of renormalization of Green's function resulting from intra-and inter-orbital flips of tunneling electrons.…”

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