## PHASE TRANSITIONS IN STRONGLY CORRELATED ELECTRON SYSTEMS. EXACTLY SOLVABLE MODELS

### Ihor Stasyuk

##### Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine

Some problems of the theory of strongly correlated electron systems are discussed in the lecture. A brief review of the history of the main ideas and model development (from the Bogoliubov polar model of the metal, Hubbard model and its extensions to the Falicov-KimbaJl and pseudospin-electron models) is given.
The dynamical mean field theory (DMFT) approach, which is exact hi the limit of the infinite dimension of space, is presented on the example of the binary alloy lattice model. It provides a derivation of equations for the coherent potential and electron Green’s function in an analytic
form as well as expressions for the grand canonical potential and static susceptibilities in the cases of the exactly solvable models.
Besides the binary alloy model the pseudospin-electron model (PEM) and Falicov-Kimball (FK) one belong to the models of this kind. The results of recent investigations of the FK model performed by various groups are discussed. The main features of the energy spectrum and thermodynamics of the model as well as phase transitions into modulated or segregated phases are considered.
Special attention is paid in the lecture to the pseudospin-electron model which appeared in the last few years in connection with the investigation of the high-Tc superconductors and systems with hydrogen bonds (the model is closely related to the FK model but differs by the regime of the thermodynamical averaging procedure). The results of investigation of the equilibrium states of PEM (using its various versions) within the DMFT scheme and by means of the generalized random phase approximation are analyzed and compared. The possibilities of applica-i ion of the PEM to description of the inhomogeneous states and structure instabilities in the high-Tc super-conducting systems are discussed.

* Personal webpage *