Wilson’s numerical renormalization group method for the calculation of dynamic properties of impurity models is generalized to investigate the effective impurity model of the dynamical mean-field theory at finite temperatures. We calculate the spectral function and self-energy for the Hubbard model on a Bethe lattice with infinite coordination number directly on the real-frequency axis and investigate the phase diagram for the Mott-Hubbard metal-insulator transition. While for $T<\mathrm{}{T}_{\mathrm{c}}\approx 0.02W$ $(W:$ bandwidth) we find hysteresis with first-order transitions both at $U_{\mathrm{c}1\mathrm{}}$ (defining the insulator to metal transition) and at $U_{\mathrm{c}2\mathrm{}}$ (defining the metal to insulator transition), at $T>\mathrm{}{T}_{\mathrm{c}}$ there is a smooth crossover from metalliclike to insulatinglike solutions.

• Received 19 December 2000

DOI:https://doi.org/10.1103/PhysRevB.64.045103