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 Uc = 4.43 ± 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. PACS. 71.10Fd Lattice fermion models (Hubbard model, etc.) – 71.27.+a Strongly correlated electron systems; heavy fermions – 71.30+h Metal-insulator transitions and other electronic transitions