The Mott transition in the strong coupling perturbation theory

Abstract

Using the strong coupling diagram technique a self-consistent equation for the electron Green's function is derived for the repulsive Hubbard model. Terms of two lowest orders of the ratio of the bandwidth $\Delta$ to the Hubbard repulsion $U$ are taken into account in the irreducible part of the Larkin equation. The obtained equation is shown to retain causality and gives the correct result in the limit $U\to 0$. Calculations were performed for the semi-elliptical initial band. It is shown that the approximation describes the Mott transition, which occurs at $U_c=\sqrt{3}\Delta /2$. This value coincides with that obtained in the Hubbard-III approximation. At small deviations from half-filling the density of states shifts along the frequency axis without perceptible changes in its shape. For larger deviations the density of states is modified: it is redistributed in favor of the subband, in which the Fermi level is located, and for $U>U_c$ the Mott gap disappears.

7 pages, 5 figures

References in corpus (4)

• Fluctuating charge density waves in the Hubbard model
• Quasiparticle states of the Hubbard model near the Fermi level
• Magnetic susceptibility of the two-dimensional Hubbard model using a power series for the hopping constant
• Numerical Studies of the 2D Hubbard Model

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• The Hubbard model in the strong coupling theory at arbitrary filling
• Properties of the half-filled Hubbard model investigated by the strong coupling diagram technique
• Continuum of many-particle states near the metal-insulator transition in the Hubbard model
• The Hubbard model in strong magnetic field: Low-frequency quantum oscillations due to strong electron correlations
• Quasi-particle propagation across semiconductor-Mott insulator interfaces
• Spin and charge fluctuations in the Hubbard model