强关联电子系统中的量子场论

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《强关联电子系统中的量子场论》是由世界图书出版公司出版的。

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research on electronic systems in condensed matter physics is at present developing very rapidly, where the main focus is changing from the "single-particle problem" to the "many-particle problem". that is, the main research interest changed from phenomena that can be understood in the single particle picture, as, for example, in band theory, to phenomena that arise owing to the interaction between many electrons.

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插图：On the other hand, there exist modes that are only contributed by a limited area of the Fermi surface, being local in k-space (individual excitation). These excitations build up a continuum spectrum, and are not very much influenced by the effect of the interaction. Putting it the other way round, also without interaction, individual excitations; that is, electron-hole pair creations emerges. In the higher-dimensional case, because both modes exist and the ratio of the individual excitations is larger, the excitation spectrum does not change drastically when no interaction is present. This corresponds to the Fermi liquid. However, in the one-dimensional case, the 'Fermi surface' consists only of the two points kF and ——kF, and therefore only the collective excitation modes exist. Therefore, the effect of the correlation is drastically visible. For this reason, the one-dimensional system is a non-Fermi liquid. We conclude that from the point of view where the Fermi surface is considered to be a dynamic variable, the Tomonaga Luttinger liquid and the Fermi liquid can be described using almost the same physical picture.However, in higher dimensions it is not easy to treat the Umklapp scattering by the bosonization scheme. In the Mott insulator, Umklapp scattering certainly occurs, and for this reason, in the vicinity of the Mott insulator state, perhaps a non-Fermi liquid arises. This problem is related to thehigh temperature superconductors, and is at present being intensively investigated.