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We investigate the Anderson-Holstein model with strong repulsion of impurity electrons using a strongcoupling approximation. The strong electron-phonon interaction determines the formation of polarons with heavy clouds of phonons surrounding the impurity electrons. We describe the collective mode of phonon clouds and the relation between electron propagators and correlation functions. We obtain the dependence of the collective mode energy on the hybridization parameter in the case T = 0 and prove that it is suppressed by increasing hybridization. [ABSTRACT FROM AUTHOR]

We investigate the minimal model that takes orbital degrees of freedom into account: the degenerate two-orbital 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We consider the four-band model of high-temperature superconductors with copper $$3d_{x^2 - y^2 } $$ and 4 s electrons and oxygen 2 p x and 2 p y electrons. We assume that the Coulomb repulsion between the copper 3 d electrons is strong. We diagonalize the oxygen subsystem and pass to the Wannier representation for the CuO 2 cluster. We study the properties of a local cell model and find its low-energy states such as the one-particle doublet and the two-particle singlet and triplet states. We consider the cell fermion delocalization because of their tunneling between the copper sites. We obtain a system of Dyson-type equations for renormalized one-particle Green’s functions and discuss whether it can be simplified. [ABSTRACT FROM AUTHOR]