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arXiv:cond-mat/9903245

Absence of the Mott transition in infinite dimensions

Kurt Fischer

Published Mar 16, 1999• 0 citations
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Abstract

It is shown that the half filled Hubbard model does not display the Mott metal-insulator transition, in the limit of infinite dimensions. The proposed transition on the Bethe lattice is proved to be an artifact. In the atomic limit, the model is always in the antiferromagnetic phase, which can be described by the Weiss mean field model.
DOI
10.48550/arxiv.cond-mat/9903245

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We study the Hubbard model in infinite dimension d= infinity within an approximation reproducing simultaneously the atomic limit and the weak-coupling limit up to second order in the interaction strength U. Depending on U we find a paramagnetic metal, a paramagnetic insulator, or an antiferromagnetic insulator. The stability of the antiferromagnetic phase is investigated by calculating the grand canonical potential. We present the phase diagram in the T-U plane and results for the magnetization m as a function of temperature T. For small values of U the antiferromagnetic phase transition is continuous, but for larger values of U the approximation yields a first-order magnetic phase transition. Results for the density of states N( epsilon ) are presented; it either exhibits one single band or an upper and a lower Hubbard band separated by the Mott gap. The upper and lower Hubbard band may exhibit additional magnetic structure, depending on the value of T and U.
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