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

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

2003-03-05

arxiv.org/abs/cond-mat/0303085v2

Eur. Phys. J. B 35, 155 (2003)

Physics

Condensed Matter

Strongly Correlated Electrons

22 pages, 16 figures; minor changes (one reference added, included comparison with Falicov-Kimball model)

Scientific paper

10.1140/epjb/e2003-00266-4

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 $\alpha=1/2$ 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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