Quantitative Aspects of the Dynamical CPA in Harmonic Approximation

TL;DR

This study evaluates the dynamical CPA combined with harmonic approximation for the Hubbard model in high dimensions, showing it accurately predicts magnetic properties and transition points, but requires higher-order corrections at low temperatures.

Contribution

It demonstrates the quantitative accuracy of the dynamical CPA+HA in describing magnetic properties and phase transitions in high-dimensional Hubbard models.

Findings

Accurately reproduces sublattice magnetization and susceptibilities.

Predicts Néel and Curie temperatures consistent with QMC results.

Identifies the need for higher-order corrections at low temperatures for MI transition.

Abstract

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 magnetization, the magnetizations, susceptibilities, and the N\'eel temperatures ($T_{\rm N}$) as well as the Curie temperatures calculated by the Quantum Monte-Carlo (QMC) method. The critical Coulomb interactions ($U_{\rm c}$) for the metal-insulator (MI) transition are also shown to agree with the QMC results above $T_{\rm N}$. Below $T_{\rm N}$, $U_{\rm c}$ 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.