Many Particle Strongly Interacting Systems.pdf

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search on electronic properties of solids is the development of variety of the
new classes of materials with unusual properties: high-Tc superconductors,
heavy fermion compounds, complex oxides, diluted magnetic semiconductors, perovskite manganites, etc. Contrary to simple metals, where the fundamentals are very well known and the electrons can be represented so that
they weakly interact with each other, in these materials, the electrons interact strongly, and moreover their spectra are complicated, i.e. have many
branches. This gives rise to interesting phenomena [16] such as magnetism,
metal-insulator transition in oxides, heavy fermions, colossal negative magnetoresistance in manganites, etc., but the understanding of what is going
on is in many cases only partial.
The subject of the present paper is a microscopic many-body theory of
strongly correlated electron models. A principle importance of these studies is concerned with a fundamental problem of electronic solid state theory,
namely with the tendency of 3d(4d) electrons in transition metal compounds
and 4f(5f) electrons in rare-earth metal compounds and alloys to exhibit
both the localized and delocalized (itinerant) behaviour. Interesting electronic and magnetic properties of these substances are intimately related to
this dual behaviour of electrons[17]-[19].
The problem of adequate description of strongly correlated electron systems
has been studied intensively during the last decade[20],[21], especially in
context of the physics of magnetism, heavy fermions and high-Tc superconductivity [7]. The understanding of the true nature of electronic states and
their quasi-particle dynamics is one of the central topics of the current experimental and theoretical studies in the field. A plenty of experimental
and theoretical results show that this many-body quasi-particle dynamics
is quite nontrivial. A vast amount of theoretical searches for a suitable description of strongly correlated fermion systems deal with simplified model
Hamiltonians. These include, as workable patterns, the single-impurity Anderson model (SIAM) and Hubbard model. In spite of certain drawbacks,
these models exhibit the key physical feature: the competition and interplay
between kinetic energy (itinerant) and potential energy (localized) effects.
A fully consistent theory of quasi-particle dynamics of both the models is
believed to be crucially important for a deeper understanding of the true
nature of electronic states in the above-mentioned class of materials. In
spite of experimental and theoretical achievements, it remains still much to
be understood concerning such systems [18],[22].
Recent theoretical investigations of strongly correlatedsystems have brought
forth a significant variety of the approaches to solve these controversial problems. There is an important aspect of the problem under consideration,
namely, how to take adequately into account the lattice (quasi-localized)
character of charge carriers, contrary to simplified theories of the type of a
weakly interacting electron gas. To match such a trend, we need to develop
a systematic theory of correlated systems, to describe, from the first princi4