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 <InlineEquation ID="Equ1"> <EquationSource Format="TEX">$U_{\rm c}=4.43 \pm 0.05$</EquationSource> </InlineEquation>. Moreover, the density of states near the gap increases algebraically as a function of frequency with an exponent <InlineEquation ID="Equ2"> <EquationSource Format="TEX">$\alpha=1/2$</EquationSource> </InlineEquation> 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. Copyright Springer-Verlag Berlin/Heidelberg 2003