11 research outputs found
Quasiparticle states of the Hubbard model near the Fermi level
The spectra of the t-U and t-t'-U Hubbard models are investigated in the
one-loop approximation for different values of the electron filling. It is
shown that the four-band structure which is inherent in the case of
half-filling and low temperatures persists also for some excess or deficiency
of electrons. Besides, with some departure from half-filling an additional
narrow band of quasiparticle states arises near the Fermi level. The dispersion
of the band, its bandwidth and the variation with filling are close to those of
the spin-polaron band of the t-J model. For moderate doping spectral
intensities in the new band and in one of the inner bands of the four-band
structure decrease as the Fermi level is approached which leads to the
appearance of a pseudogap in the spectrum.Comment: 8 pages, 7 figure
Interaction of strongly correlated electrons and acoustical phonons
We investigate the interaction of correlated electrons with acoustical
phonons using the extended Hubbard-Holstein model in which both, the
electron-phonon interaction and the on-site Coulomb repulsion are considered to
be strong. The Lang-Firsov canonical transformation allows to obtain mobile
polarons for which a new diagram technique and generalized Wick's theorem is
used. This allows to handle the Coulomb repulsion between the electrons emerged
into a sea of phonon fields (\textit{phonon clouds}). The physics of emission
and absorption of the collective phonon-field mode by the polarons is discussed
in detail. Moreover, we have investigated the different behavior of optical and
acoustical phonon clouds when propagating through the lattice. In the
strong-coupling limit of the electron-phonon interaction, and in the normal as
well as in the superconducting phase, chronological thermodynamical averages of
products of acoustical phonon-cloud operators can be expressed by one-cloud
operator averages. While the normal one-cloud propagator has the form of a
Lorentzian, the anomalous one is of Gaussian form and considerably smaller.
Therefore, the anomalous electron Green's functions can be considered to be
more important than corresponding polarons functions, i.e., pairing of
electrons without phonon-clouds is easier to achieve than pairing of polarons
with such clouds.Comment: : 28 pages, 9 figures, revtex4. Invited paper for a special issue of
Low Temperature Physics dedicated to the 20th anniversary of HTS
Diagrammatic analysis of the Hubbard model:Stationary property of the thermodynamic potential
Diagrammatic approach proposed many years ago for strong correlated Hubbard
model is developed for analyzing of the thermodynamic potential properties. The
new exact relation between such renormalized quantities as thermodynamic
potential, one-particle propagator and correlation function is established.
This relation contains additional integration of the one-particle propagator by
the auxiliary constant. The vacuum skeleton diagrams constructed from
irreducible Green's functions and tunneling propagator lines are determined and
special functional is introduced. The properties of such functional are
investigated and its relation to the thermodynamic potential is established.
The stationary properties of this functional with respect to first order
changing of the correlation function is demonstrated and as a consequence the
stationary properties of the thermodynamic potential is proved.Comment: 6 pages, 4 figure
Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons
We investigate the interaction of strongly correlated electrons with phonons
in the frame of the Hubbard-Holstein model. The electron-phonon interaction is
considered to be strong and is an important parameter of the model besides the
Coulomb repulsion of electrons and band filling. This interaction with the
nondispersive optical phonons has been transformed to the problem of mobile
polarons by using the canonical transformation of Lang and Firsov. We discuss
in particular the case for which the on-site Coulomb repulsion is exactly
cancelled by the phonon-mediated attractive interaction and suggest that
polarons exchanging phonon clouds can lead to polaron pairing and
superconductivity. It is then the frequency of the collective mode of phonon
clouds being larger than the bare frequency, which determines the
superconducting transition temperature.Comment: 23 pages, Submitted to Phys. Rev.
Diagrammatic theory for Anderson Impurity Model. Stationary property of the thermodynamic potential
A diagrammatic theory around atomic limit is proposed for normal state of
Anderson Impurity Model. The new diagram method is based on the ordinary Wick's
theorem for conduction electrons and a generalized Wick's theorem for gtrongly
correlated impurity electrons. This last theorem coincides with the definition
of Kubo cumulants. For the mean value of the evolution operator a linked
cluster theorem is proved and a Dyson's type equations for one-particle
propagators are established. The main element of these equations is the
correlation function which contains the spin, charge and pairing fluctuations
of the system. The thermodynamic potential of the system is expressed through
one-particle renormalized Green's functions and the corelation function. The
stationary property of the thermodynamic potential is established with respect
to the changes of correlation function.Comment: 7 pages, 6 figures, Submitted to PR
Diagrammatic theory for Periodic Anderson Model: Stationary property of the thermodynamic potential
Diagrammatic theory for Periodic Anderson Model has been developed, supposing
the Coulomb repulsion of localized electrons as a main parameter of the
theory. electrons are strongly correlated and conduction electrons
are uncorrelated. Correlation function for and mass operator for
electrons are determined. The Dyson equation for and Dyson-type equation
for electrons are formulated for their propagators. The skeleton diagrams
are defined for correlation function and thermodynamic functional. The
stationary property of renormalized thermodynamic potential about the variation
of the mass operator is established. The result is appropriate as for normal
and as for superconducting state of the system.Comment: 12 pages, 10 figure
Stationary property of the thermodynamic potential of the Hubbard model in strong coupling diagrammatic approach for superconducting state
Diagrammatic analysis for normal state of Hubbard model proposed in our previous paper is generalized and
used to investigate superconducting state of this model. We use the notion of charge quantum number to describe
the irreducible Green's function of the superconducting state. As in the previous paper we introduce the notion of
tunneling Green's function and of its mass operator. This last quantity turns out to be equal to correlation function
of the system. We proved the existence of exact relation between renormalized one-particle propagator and
thermodynamic potential which includes integration over auxiliary interaction constant. The notion of skeleton
diagrams of propagator and vacuum kinds were introduced. These diagrams are constructed from irreducible
Green's functions and tunneling lines. Identity of this functional to the thermodynamic potential has been proved
and the stationarity with respect to variation of the mass operator has been demonstrated