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Physical Review Letters

Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension

Élliott H. Lieb, Fa Yueh Wu

Published Jun 17, 1968• 2,941 citations
Publisher

Abstract

The short-range, one-band model for electron correlations in a narrow energy band is solved exactly in the one-dimensional case. The ground-state energy, wave function, and the chemical potentials are obtained, and it is found that the ground state exhibits no conductor-insulator transition as the correlation strength is increased.
DOI
10.1103/physrevlett.20.1445

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The ground-state wave function for the electrons in a narrow sss band is investigated for arbitrary density of electrons and arbitrary strength of interaction. An approximation is proposed which limits all the calculations to counting certain types of configurations and attaching the proper weights. The expectation values of the one-particle and two-particle density matrix are computed for the ferromagnetic and for the non-ferromagnetic case. The ground-state energy is obtained under the assumption that only the intra-atomic Coulomb interaction is of importance. Ferromagnetism is found to occur if the density of states is large at the band edges rather than in the center, and if the intra-atomic Coulomb repulsion is sufficiently strong. The relation of this approximation to certain exact results for one-dimensional models is discussed.
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