This book provides the first systematic discourse on a very peculiarapproach to the theory of strongly correlated systems. HubbardX-operators have been known for a long time but have not been widelyused because of their awkward algebra. The book shows that it ispossible to deal with X-operators even in the general multilevel localeigenstate system, and not just in the case of the nondegenerateHubbard model. X-operators provide the natural language for describingquasiparticles in the Hubbard subbands with unusual doping andtemperature-dependent band structures.

The application of high pressure affects the band structure and magnetic interactions in solids by modifying nearest-neighbor distances and interatomic potentials. While all materials experience electronic changes with increasing pressure, spin polarized, strongly electron correlated materials are expected to undergo the most dramatic transformations. In such materials, (d and f-electron metals and compounds), applied pressure reduces the strength of on-site correlations, leading to increased electron delocalization and, eventually, to loss of its magnetism. In this ongoing project, we study the electronic and magnetic properties of Group VIII, 3d (Fe, Co and Ni) magnetic transition metals and their compounds at high pressures. The high-pressure properties of magnetic 3d-transition metals and compounds have been studied extensively over the years, because of iron being a major constituent of the Earth's core and its relevance to the planetary modeling to understand the chemical composition, internal structure, and geomagnetism. However, the fundamental scientific interest in the high-pressure properties of magnetic 3d-electron systems extends well beyond the geophysical applications to include the electron correlation-driven physics. The role of magnetic interactions in the stabilization of the ''non-standard'' ambient pressure structures of Fe, Co and Ni is still incompletely understood. Theoretical studies have predicted (and high pressure experiments are beginning to show) strong correlations between the electronic structure and phase stability in these materials. The phase diagrams of magnetic 3d systems reflect a delicate balance between spin interactions and structural configuration. At ambient conditions, the crystal structures of [alpha]-Fe(bcc) and {var_epsilon}-Co(hcp) phases depart from the standard sequence (hcp → bcc→ hcp → fcc), as observed in all other non-magnetic transition metals with increasing the d-band occupancy, and are different from those of their 4d- and 5d-counter parts. This anomalous behavior has been interpreted in terms of the spin-polarized d-band altering the d-band occupancy [1]. At high pressures, however, the d-valence band is expected to broaden resulting in a suppression or even a complete loss of magnetism. Experimentally, ferromagnetic [alpha](bcc)-Fe has been confirmed to transform to non-magnetic {var_epsilon}-Fe (hcp) at 10 GPa [2,3]. Recently, we have also observed a similar transition in Co from ferromagnetic [alpha](hcp)-Co to likely nonmagnetic [beta](fcc)-Co at 105 GPa[4]. A similar structural phase transition is expected in Ni, probably in the second-order fcc-fcc transition. However, there has been no directly measured change in magnetism associated with the structural phase transition in Co, nor has yet been confirmed such an iso-structural phase transition in Ni. Similar electronic transitions have been proposed in these 3d-transition metal oxides (FeO, CoO and NiO) from high spin (magnetic) to low spin (nonmagnetic) states [5]. In each of these systems, the magnetic transition is accompanied by a first-order structural transition involving large volume collapse (10% in FeO, for example). So far, there have been no electronic measurements under pressure confirming these significant theoretical predictions, although the predicted pressures for the volume collapse transitions are within the experimental pressure range (80-200GPa).

Recent advances in high pressure diamond anvil cell techniques and synchrotron radiation characterization methods have enabled investigation of a wide range of materials properties in-situ under extreme conditions. High pressure studies have made significant contribution to our understanding in a number of scientific fields, e.g. condensed matter physics, chemistry, Earth and planetary sciences, and material sciences. Pressure, as a fundamental thermodynamic variable, can induce changes in the electronic and structural configuration of a material, which in turn can dramatically alter its properties. The novel phases and new compounds existing at high pressure have improved our basic understanding of bonding and interactions in condensed matter. This dissertation focuses on how pressure affects materials' bonding and electronic structures in two types of systems: hydrogen rich molecular compounds and strongly correlated transition metal oxides. The interaction of boranes and hydrogen was studied using optical microscopy and Raman spectroscopy and their hydrogen storage potential is discussed in the context of practical applications. The pressure-induced behavior of the SiH4 + H2 binary system and the formation of a newly formed compound SiH4(H2)2 were investigated using a combination of optical microscopy, Raman spectroscopy and x-ray diffraction. The experimental work along with DFT calculations on the electronic properties of the compound up to the possible metallization pressure, indicated that there are strong intermolecular interactions between SiH4 and H2 in the condensed phase. By using a newly developed synchrotron x-ray spectroscopy technique, we were able to follow the evolution of the 3d band of a 3d transition metal oxide, Fe2O3 under pressure, which experiences a series of structural, electronic and spin transitions at approximately 50 GPa. Together with theoretical calculations we revisited its electronic phase transition mechanism, and found that the electronic transitions are reflected in the pre-edge region.

Electronic structure and physical properties of strongly correlated materials containing elements with partially filled 3d, 4d, 4f and 5f electronic shells is analyzed by Dynamical Mean-Field Theory (DMFT). DMFT is the most universal and effective tool used for the theoretical investigation of electronic states with strong correlation effects. In the present book the basics of the method are given and its application to various material classes is shown. The book is aimed at a broad readership: theoretical physicists and experimentalists studying strongly correlated systems. It also serves as a handbook for students and all those who want to be acquainted with fast developing filed of condensed matter physics.