Analytical and numerical treatment of the Mott-Hubbard insulator in infinite dimensions

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-c=4.43+/-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.