Mott-Hubbard model

It is believed that electron correlation plays an important role with the anomalously high resistivity exhibited in marginal metals. Unfortunately, although the Mott-Hubbard model adequately explains behavior on the insulating side of the M-NM transition, on the metallic side, it does so only if the system is far from the transition. Electron dynamics of systems in which U is only slightly less than W (i.e. metallic systems close to the M-NM transition), are not well described by a simple itinerant or localized picture. The study of systems with almost localized electrons is still an area under intense investigation within the condensed matter physics community. A dynamical mean field theory (DMFT) has been developed for the Hubbard model, which enables one to describe both the insulating state and the metallic state, at least for weak correlation. 

For transition metal oxides such as NiO the Mott-Hubbard model gives much better agreement with experiment localization of the electrons in this way explains the anh-ferromagnetic ordering observed in NiO and its electrical insulator proper-hes [112]. The terms required to calculate the electron-electron interachon energy on a site, Fmh can be written in terms of the d-electron occupahons, using a UHF approach ... 

Of course some of these interaction terms are already present in an LSDA calculation and so to incorporate this into a general DFT scheme requires these duplicate contributions to be removed. One way to do this has been proposed by Dudarev and coworkers [113]. They have derived a funchonal incorporating the U and J parameters of the Mott-Hubbard model which is written ... 

Fig. 7 a-c. Schematic representation of final state screening models for lanthanide and d-metal core level responses (a) and c)) (c.b. means conduction band). In part b), the possible situations for light and heavy actinides (before and after the Mott-Hubbard transition) are also represented... 

Within the actinide series Pu is the most intriguing element. On the basis of the Hubbard model, and taking into account an unhybridized bandwidth Wf (due only to f-f overlapping), the Un/Wf ratio is 0.7 for U and 3 for Pu in fact, one would have expected already for Pu a 5 f electron localization, since Uh > Wf. However, a hybridization of 5 f with (6d7s) states broadens the 5f bandwidth and delays the Mott-like transition (see Chap. A) from Pu to Am This influences many properties of Pu metaf . ... 

A fundamental question is whether the transition between localized and itinerant electronic behavior is continuous or discontinuous. Mott (1949) was the first to point out that an on-site electrostatic energy Ua > Wr, is needed to account for the fact that NiO is an antiferromagnetic insulator rather than a metal. Hubbard (1963) subsequently introduced U formally as a parameter into the Hamiltonian for band electrons his model predicted a smooth transition from a Pauli paramagnetic metal to an antiferromagnetic insulator as the ratio W/U decreased to below a critical value of order unity. This metal-insulator transition is known as the Mott-Hubbard transition. 

A systematic semiempirical study of the core-level photoemission spectra of a wide range of 3d transition-metal compounds has been carried out (Bocquet et al., 1992,1996). The values for U and A obtained from a simplified Cl cluster model analysis are demonstrated in Figure 7.2. As can be inferred from the graphs, the heavier 3d transition metal compounds shown in the figure are expected to be charge-transfer insulators, whereas the compounds of the fighter metals are generally expected to be of the Mott-Hubbard type. 

This signals the presence of a gap Ap-Tp in the charge degrees of freedom, which has the same origin as the Mott-Hubbard gap in the one-dimensional Hubbard model at half-filling [119]. 

When the long-range Coulomb interaction is small, one can take account of only the on-site Coulomb interaction energy U between two electrons on a molecule. This electronic system is described in terms of the Hubbard model. Theoretical studies have shown that for UtW > 1 the electrons undergo the Mott transition which does not necessarily involve any structural changes. The electrons are localized with equal distance. They are apparently the same as the Wigner crystal described above. It is shown that the Mott transition is easy to occur when the charge density is l/molecule or I/site. 

Park J-H, Woodward PM, Parise JB (1998) Predictive modeling and high pressure-high temperature synthesis of perovskites containing Ag. Chem Mater 10 3092-3100 Pasternak MP, Rozenberg GK, Machavariani GY, Naaman O, Taylor RD, Jeanloz R (1999) Breakdown of the Mott-Hubbard state in Fc203 A first-order insulator-metal transition with collapse of magnetism at 50 GPa. Phys Rev Lett 82 4663-4666... 

The first section of the chapter deals with various theoretical models. The computational realization of these models will also be discussed in the context of modern computer technology. Applications are discussed in terms of complex physical structures (silicate crystals, defects, surfaces) where the problems are largely technical, and complex electronic structure (Mott-Hubbard insulators) where fundamental questions about electron interactions are relevant. 

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