This book provides the first systematic discourse on a very peculiar approach to the theory of strongly correlated systems. Hubbard X-operators have been known for a long time but have not been widely used because of their awkward algebra. The book shows that it is possible to deal with X-operators even in the general multilevel local eigenstate system, and not just in the case of the nondegenerate Hubbard model. X-operators provide the natural language for describing quasiparticles in the Hubbard subbands with unusual doping and temperature-dependent band structures.The X-operator diagram technique is presented in detail, so that a newcomer with knowledge of the usual Fermi/Bose operator diagram technique can use the former after reading the book.Examples are taken from the theory of high-Tc superconductivity, rare-earth compounds with strong magnetic anisotropy and quantum oscillations in strongly correlated systems.
Hubbard Model as the Simplest Model of Strong Electron Correlation; Multielectron Models in X-Operators Representation; General Approach to the Quasiparticle Description of Strongly Correlated Systems; Unitary Transformations Method in Atomic Representation; Diagram Technique in the X-Operators Representation; Spectral Properties of the Anisotropic Metallic Ferromagnets; Peculiarities of the de Haas-van Alphen Effect in Strongly Correlated Systems with Magnetic Polaron States; The Electronic Structure of Copper Oxides in the Multiorbital p-d Model