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Analytical and Numerical Treatment of the Mott--Hubbard Insulator in Infinite Dimensions

Michael P. Eastwood·Florian Gebhard·Eva Kalinowski·Satoshi Nishimoto·Reinhard M. Noack
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Abstract

We calculate the density of states in the half-filled Hubbard model on a Bethe lattice with infinite connectivity. Based on our analytical results to second order in $t/U$, we propose a new `Fixed-Energy Exact Diagonalization' scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated by results from the Random Dispersion Approximation, we find that the gap opens at $U_{\rm c}=4.43 \pm 0.05$. Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent $α=1/2$ in the insulating phase. We critically examine other analytical and numerical approaches and specify their merits and limitations when applied to the Mott--Hubbard insulator.

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Michael P. Eastwood, Florian Gebhard, Eva Kalinowski, Satoshi Nishimoto, Reinhard M. Noack. 2003-10-02. Analytical and Numerical Treatment of the Mott--Hubbard Insulator in Infinite Dimensions. https://doi.org/10.1140/epjb%2Fe2003-00266-4

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