Recently it was proved that the Majumdar-Ghosh chain with the Hamiltonian has at least two ground states, in which the spins are arranged in nearest-neighbour singlet pairs. In this work it is shown that these two states are the only ground states. Besides, a rapidly converging variational method is given to determine the elementary excitations.
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IPreface.As a work of theoretical physics this monograph is intended for two groups of readers:-the theorists who want to have an introduction in the field of spin models, especially those which allow for a (partially) exact solution, and -the solid-state physicists who wish to orient themselves in the field of spin systems as models for magnetic lattices. The theorist will find references to the literature in those examples in which the author has chosen to restrict himself in the exposition of mathematical details. But they may profit from an overall picture of exact results for those spin models that are most relevant in the author's view. This group of readers may find in a relatively short time the way to the front of this special field of research, which has recently found new impulses from the endeavour to understand high-T c superconductivity.The level of sophistication of this monograph makes it possible for the experimentalist with a basic knowledge of quantum mechanics to get an insight in the properties of well-known quantum-spin models within reasonable time. Knowledge of this field seems to become more and more a prerequisite for the understanding of a variety of quantum effects in the solid state.In avoiding special mathematical techniques the author hopes to induce a cooperation between both groups of potential readers, in those cases in which such a cooperation seems to be essential in keeping up with the results of rapidly developing fields, like the already mentioned high-T c superconductivity.This work reflects the state of the art at this moment and presents a lot of unsolved questions. In the author's view this is a situation typical of a flourishing part of theoretical physics that may attract the interest of many more generations to come.The author welcomes suggestions for improvement of the general plan of his book and also corrections of simple mistakes.
W. J. Caspers
Exact expressions are derived for some excited states in a linear quantum spin system for which the exact ground state has been studied in the last decade.
The energy spectrum and the correlation functions for n electrons in the one-dimensional single band Hubbard model with periodic boundary conditions are calculated exactly. For that purpose the Hamiltonian is transformed into a set of Hamiltonians, corresponding to systems of spinless fermions. Our results include the results of Mei and Chen, presented in a recent paper.
The problem of the determination of the macroscopic conductivity of statistically homogeneous and isotropic polycrystalline materials in terms of the principal values of the conductivity tensor of the constituent crystals is considered. A perturbation expansion, in terms of correlation functions with an optimal value of the zeroth-order estimate of the effective conductivity, is derived in which a separation is established into texture dependent and independent quantities. Consistence with the analogous expansion for the effective resistivity is demonstrated.
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