Quantitative Aspects of the Dynamical Coherent Potential Approximation in Harmonic Approximation

Magnetic and electronic properties of the Hubbard model on the Bethe and fcc lattices in infinite dimensions have been investigated numerically on the basis of the dynamical coherent potential approximation (CPA) theory combined with the harmonic approximation (HA) in order to clarify the quantitative aspects of the theory. It is shown that the dynamical CPA+HA reproduces well the sublattice magnetizations, the magnetizations, susceptibilities, and the Néel temperatures ($T_{\text{N}}$) as well as the Curie temperatures calculated by the Quantum Monte-Carlo (QMC) method. The critical Coulomb interactions ($U_{\text{c}}$) for the metal--insulator (MI) transition are also shown to agree with the QMC results above $T_{\text{N}}$. Below $T_{\text{N}}$, $U_{\text{c}}$ deviate from the QMC values by about 30% at low temperature regime. These results indicate that the dynamical CPA+HA is applicable to the quantitative description of the magnetic properties in high dimensional systems, but one needs to take into account higher-order dynamical corrections in order to describe the MI transition quantitatively at low temperatures.