Dynamical response functions of the Hubbard model on an infinite dimensional lattice (D=∞) are investigated by the self-consistent second-order perturbation theory with respect to the Coulomb interaction U. The vertex corrections are properly considered so that the conservation laws are satisfied, i.e., the f-sum rule is satisfied. The explicit expression for the f-sum rule is obtained in the case of infinite dimensions. It is found that even in the second-order perturbation theory the electronic states show many-body features at finite temperature and/or frequency regions: the system crosses over from the Fermi-liquid state at the low temperature and low-frequency region to the incoherent regime at high temperatures.

• Received 4 March 1993

DOI:https://doi.org/10.1103/PhysRevB.47.15428