by S G Ovchinnikov (LV Kirensky Institute of Physics, Siberian Branch of the Russian Academy of Sciences & Krasnoyarsk State Technical University, Russia) & V V Val'kov (LV Kirensky Institute of Physics, Siberian Branch of the Russian Academy of Sciences & Krasnoyarsk State Technical University, Russia)

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 a Simplest Model of Strong Electron Correlations
• Multielectron Models in X-Operator Representation
• General Approach to the Quasiparticle Description of Strongly Correlated Systems
• Unitary Transformation Method in Atomic Representation
• Diagram Technique in the X-Operators Representation
• Spectral Properties of 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