Quantum Many-Body Theory and Coherent Potential Approximation

Abstract

The coherent potential approximation (CPA) is a useful method for describing the electron correlations as well as the effects of disorder on electrons. Among the many-body theories using the CPA, the dynamical CPA, the many-body CPA, and the dynamical mean-field theory are reviewed to clarify how these theories use the CPA concept for the description of the electron correlations. The theories characterized by the momentum independent self-energy are shown to interpolate between the weak and strong Coulomb interaction limits, and therefore describe the basic properties of magnetism from metals to insulators, the metalinsulator transition, and the single particle excitations from the Fermi liquid to the insulator. The relation among various theories are clarified. In particular, it is shown that the dynamical CPA, the many-body CPA, and the dynamical mean-field theory are equivalent to each other, so that the theories of itinerant magnetism and those of the strongly correlated electron systems are unified within the single-site approximation. The nonlocal effects on the selfenergy are also discussed beyond the single-site approximation.