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.

We propose a diagram theory around the atomic limit for the single-impurity Anderson model in which the strongly correlated impurity electrons hybridize with free (uncorrelated) conduction electrons. Using this diagram approach, we prove a linked-cluster theorem for the vacuum diagrams and derive Dyson-type equations for localized and conduction electrons and the corresponding equations for mixed propagators. The system of equations can be closed by summing an infinite series of ladder diagrams containing irreducible Green's functions. The result allows discussing resonances associated with quantum transitions at the impurity site.

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.

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We investigate the minimal model that takes orbital degrees of freedom into account: the degenerate twoorbital Hubbard model. Our consideration includes the intraatomic Coulomb interaction of two electrons with opposite spins on the same orbital and on different orbitals and interorbital hopping of tunneling electrons. We take the influence of states caused by Hund's rule coupling on the metal-insulator phase transition into account. We generalize the diagram theory developed for strongly correlated orbitally nondegenerate systems to the case of orbital degeneration. For the one-particle renormalized Green's function, we establish an equation of Dyson type for calculating the system spectral function using a simple approximation based on summing chain diagrams.We dedicate this paper to the memory of the outstanding Russian scientist and remarkable person Professor Sergei Vladimirovich Tyablikov, who departed us so early but whose papers and monographs [1], [2] left a deep footprint in science, contributing remarkably to the theory of magnetism, polaron theory, multiparticle physics, etc.With deep gratitude, we remember his considerable help in preparing scientific cadres for the Republic of Moldova. One of us (V. A. M.) experienced the tremendous charm of his remarkable personality firsthand. He was an example of kindness and principality and was demanding in science. His approval of someone's paper was always considered the highest endorsement.We shall remember him forever.

Предложен диаграммный подход для однопримесной модели Андерсона, в которой сильно коррелированные примесные электроны гибридизируются со свободными (некоррелированными) электронами проводимости. На основе этого диаграммного подхода доказана теорема о связных кластерах для вакуумных диаграмм и выведены уравнения типа уравнения Дайсона для локализованных электронов и электронов проводимости, а также соответствующие уравнения для смешанных пропагаторов. Систему уравнений можно замкнуть путем суммирования бесконечного ряда лестничных диаграмм, содержащих неприводимые функции Грина. Полученный результат позволяет рассматривать резонансы, связанные с квантовыми переходами в примесном узле. Ключевые слова: сильные корреляции, спектральная функция, уравнение Дайсона, функции Грина, примесная модель Андерсона.

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A special diagram technique recently proposed for strongly correlated electron systems is used to study the pecularities of a spindensity-wave (SDW) in competition with superconductivity. This method allows to formulate the Dyson equations for the renormalized electron propagators of the coexisting phases of SDW antiferromagnetism and superconductivity. We find the surprising result that triplet supercondctivity appears provided that we have coexistence of singlet superconductivity and SDW antiferromagnetism. A special ansatz, which takes into account the full Green's functions as well as the dynamical structure of the correlations, is used to establish the equations determining the gap functions and order parameters.