V. A. Moskalenko

PERTURBATION THEORY FOR THE PERIODIC ANDERSON MODEL

We investigate the system of conductivity electrons and f-localized electrons described by the periodic Anderson model. Single-site hybridization of the state of two constituent subsystems of electrons is treated as a perturbation. We develop a new diagram technique based on the use of multiparticle one-site irreducible Green’s functions for the f-electrons and the standard Wick theorem for the subsystem of conductivity electrons. We derive the Dyson equations for the one-particle Green’s functions and find the relation between these functions. These results are exact and can be used as a starting point for self-consistent approximations. In the Hubbard-I approximation, we analyze the spectrum of one-particle perturbations.

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

V. A. Moskalenko, P. Entel, L. A. Dohotaru, and R. Citro Institute of Applied Physics, Moldova Academy of Sciences, Chisinau 2028, Moldova BLTP, Joint Institute for Nuclear Research, 141980 Dubna, Russia University of Duisburg-Essen, 47048 Duisburg, Germany Technical University, Chisinau 2004, Moldova and Dipartimento di Fisica E. R. Caianiello, Universitá degli Studi di Salerno and CNISM, Unitá di ricerca di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy (Dated: April 11, 2008)

Electron-phonon interaction in strongly correlated systems

By a canonical transformation, the Hubbard model, supplemented with the Holstein interaction of localized electrons and nondispersive optical phonons, is transformed into a model where the hoppings of polarons from one lattice site into another are possible and are accompanied by the hoppings of an unbounded number of phonons. This, together with the fact that strong one-site interactions of electrons are inherent in the Hubbard model, leads to the necessity of introducing a new diagram technique based on irreducible one-site multi-particle Green’s functions or Kubo cumulants. The presence of phonons leads to renormalization of single-particle and multi-particle Green’s functions. The Dyson equation for the renormalized electron Green’s function is obtained. However, we did not manage to obtain the Dyson equation for the phonon functions due to the multiplicity of phonons taking part in the hopping. The validity of the theorem of connected diagrams is proved.

Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons

The interaction of strongly correlated electrons with phonons in the framework of the Hubbard-Holstein model is investigated. The electron-phonon interaction is considered to be strong and is an important parameter of the model, in addition to the Coulomb repulsion of electrons and the band filling. This interaction with nondispersive optical phonons is transformed to the problem of mobile polarons using the canonical transformation of Lang and Firsov. We discuss the case where the on-site Coulomb repulsion is exactly canceled by the phonon-mediated attractive interaction. It is suggested that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. The fact that the frequency of the collective mode of phonon clouds is larger than the bare frequency then determines the superconducting transition temperature.

Wannier Representation for the Three-Band Hubbard Model

We obtain the cell representation for the Hamiltonian of the d–p model. We use the Wannier orbitals for the holes belonging to the copper and oxygen ions; the orbitals are orthogonalized on the sites of the copper lattice. The first stage of calculating is diagonalizing the kinetic energy of the oxygen holes and, on this basis, introducing two diagonalizing orbitals for the oxygen fermions. These last two modes have significantly different local energies, which noticeably affect the results in the theory. The obtained Hamiltonian is represented as the sum of a main local term and a perturbation defining the delocalization of the Wannier fermions. We find the low-lying states and the corresponding energy spectrum for the local Hamiltonian. We show that introducing the diagonalizing fermions causes a significant lowering of the energy of the Zhang–Rice singlet.

Strongly correlated polarons

Abstract We investigate the interaction of strongly correlated electrons with phonons for the Hubbard–Holstein model. A new diagram technique is used in order to handle the Coulomb repulsion between the electrons. In the limit of strong electron–phonon coupling this yields a collective mode of phonon clouds surrounding the polarons

New approach to Periodic Anderson Model

A new diagram technique, previously proposed for Hubbard Model, was used for Periodic Anderson Model (PAM). This diagram technique is used for Matsubara Green functions and contains apart from the Wick product of free Green functions new contributions equal to on-site cumulants depending of the Coulomb interaction. If such cumulants are ignored we obtained so called Hubbard I approximation for PAM with 3 branches of renormalized energy spectrum of quasiparticles. They are investigated in detail and chemical potential of the system is determined.

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

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.

Diagram analysis of the Hubbard model: Stationarity property of the thermodynamic potential

The diagram approach proposed many years ago for the strongly correlated Hubbard model is developed with the aim to analyze the thermodynamic potential properties. A new exact relation between renormalized quantities such as the thermodynamic potential, the one-particle propagator, and the correlation function is established. This relation contains an additional integration of the one-particle propagator with respect to an auxiliary constant. The vacuum skeleton diagrams constructed from the irreducible Green’s functions and tunneling propagator lines are determined and a special functional is introduced. The properties of this functional are investigated and its relation to the thermodynamic potential is established. The stationarity property of this functional with respect to first-order variations of the correlation function is demonstrated; as a consequence, the stationarity property of the thermodynamic potential is proved.

The Possibility of Forming Coupled Pairs in the Periodic Anderson Model

We investigate the generalized periodic Anderson model describing two groups of strongly correlated (d- and f-) electrons with local hybridization of states and d-electron hopping between lattice sites from the standpoint of the possible appearance of coupled electron pairs in it. The atomic limit of this model admits an exact solution based on the canonical transformation method. The renormalized energy spectrum of the local model is divided into low- and high-energy parts separated by an interval of the order of the Coulomb electron-repulsion energy. The projection of the Hamiltonian on the states in the low-energy part of the spectrum leads to pair-interaction terms appearing for electrons belonging to d- and f-orbitals and to their possible tunneling between these orbitals. In this case, the terms in the Hamiltonian that are due to ion energies and electron hopping are strongly correlated and can be realized only between states that are not twice occupied. The resulting Hamiltonian no longer involves strong couplings, which are suppressed by quantum fluctuations of state hybridization. After linearizing this Hamiltonian in the mean-field approximation, we find the quasiparticle energy spectrum and outline a method for attaining self-consistency of the order parameters of the superconducting phase. For simplicity, we perform all calculations for a symmetric Anderson model in which the energies of twice occupied d- and f-orbitals are assumed to be the same.