By A Montorsi

ISBN-10: 9810205856

ISBN-13: 9789810205850

This ebook gathers a suite of reprints at the Hubbard version. the most important contributions to the topic considering that its starting place are integrated, with the purpose of supplying all scientists engaged on the version and its functions with quick access to the appropriate literature. The e-book is split into 5 elements. The introductory half is anxious with the actual foundation and motivations of the version, and incorporates a number of normally old papers. the rest 4 sections are meant to provide a coherent situation of the several methods to the version answer: distinct and rigorous statistical mechanics effects; variational tools; perturbative methods; numerical Quantum Monte Carlo and distinctive diagonalization reports. one of the functions distinctive emphasis is given to high-Tc superconductivity. each one part is preceded by means of statement notes from the editor.

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**Read e-book online The Hubbard Model (A Collection of Reprints) PDF**

This booklet gathers a suite of reprints at the Hubbard version. the most important contributions to the topic because its starting place are incorporated, with the purpose of supplying all scientists engaged on the version and its functions with quick access to the appropriate literature. The publication is split into 5 components. The introductory half is anxious with the actual beginning and motivations of the version, and incorporates a choice of normally historic papers.

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**Example text**

T h i s completely new aspect of the carried degenerate show c a s e is in all likelyhood linked not out by expansions Laeroix lhal d e g e n e r a c y have been [55|: Ihey and C y r o ! favours ferromagnetism only with ferromagnetism bol w i l h the q u e n c h ing of orbital m o m e n l in transition metals. 8. T h e orbilal superlatlice 7. Exact results for the degenerate R o l h | 5 1 | w a s the Hubbard firs! lo suggest lhal V a n V l e c k s m e c h a n i s m for f e r r o m a g n e l i s m leads lo hamillonian Ihe formation of an orbital s u p e r l a t l i c e , lhat is T h e degenerate obvious H u b b a r d hamiltonian generalization ^^(r-R,) of eqs.

8. A T W O - E L E C T R O N E X A M P L E In order to obtain a better physical understanding of the solution obtained in the preceding sections, and in particular how the band splits into two parts, it is instructive to consider the problem of two electrons moving and interacting in the manner described by the Hamiltonian (10). Essentially the same problem has been considered by Slater et al. (1953) who were mainly interested in the effect of correlations on the condition for ferromagnetism. Denote by $[i,J) the spatial wave function of an eigenstate of the two electron system, \^r(i, measuring the probability of finding one electron on atom i and the other on atom j .

31. lem of w h a l values are taken by ihe p a r a m e t e r s in which where we denole by U Ihe only non-zero quan- rather role functions, It would re presentation a natural Wannier wilh are entirely hard's firsl paper, we shall base Ihe theory upon value for 17, w h i c h is of (he order of Ihe lighl binding approximation w h i c h is k n o w n The lo figures be a metals. good starling Following poinl for transitional H u b b a r d , and in s e a r c h ol simplicity, we will first completely neglecl g e n e r a c y , and in section f> we will reintroduce the degeneracy and show that special de- effects arise from i l .

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