Diagrammatic Iteration Approach to Electron Correlation Effects

Abstract

Electron correlation is a measure of the errors that are inherent in the Hartree-Fock theory or orbital models. When the electron density is high, correlation is weak and the traditional electronic theory works well. However, at a low density of electrons correlation effects become strong and the traditional theory fails to describe the electron system correctly. Therefore, the electron correlation plays a radical role in such materials as high-temperature superconductors and heavy fermions, etc. To date, there is no agreement on how to deal with higher-order terms (correlation energy) in the series of electron’s ground state energy although a method that is termed diagrammatic iteration approach (DIA) was developed more than one decade ago by the authors of this article. That is why no consensus on the origin and mechanism of superconductivity has been engaged in superconductivity community. From the viewpoint of methodology, the DIA is indeed an approach to higher-order terms from the lower-order ones, i.e. it is a new method to show how to go beyond the random phase approximation (RPA) step by step by iteration. Here, we are logically presenting it to the community of modern physics with more analyses and hope to attract more attention to it and promote its applications.