Systems of Strongly Correlated Electrons Interacting with Each Other and with Phonons: Diagrammatic Approach

The features of materials leading to the strong correlation effect and the phenomena realized in them are considered: the metal-insulator Mott transition and high-temperature superconductivity. The history of their study is traced. Particular attention is paid to studying the role of the interorbital correlation effect and the Hund’s coupling in multiorbital systems as well as the electron-phonon interaction in systems with strong Coulomb interaction. The development of the strong coupling diagram technique is analyzed and the results obtained based on the approach used are presented.