On a Self-Consistent Approximation Procedure with Application to the Hubbard Model

Jerzy Mizia, Grzegorz Górski

K. Elk

Abstract Considering a very general derivation of Dyson's equation an approximation procedure is discussed, which exhibits a summary of different known methods. Concerning the Hubbard model a generalization of Roth's procedure follows. In particular it is possible to obtain a self‐consistent method.

Mohsen Jemaï, Peter Schuck

Coupled equations for even and odd particle number correlation functions are set up via the equation of motion method. For the even particle number case this leads to self-consistent random-phase approximation equations already known from the literature. From the equations of the odd particle number case the single-particle occupation probabilities are obtained in a self-consistent way. This is the essential new procedure of this work. Both even and odd particle number cases are based on the same correlated vacuum and, thus, are coupled equations. Applications to the Lipkin model and to the one-dimensional Hubbard model give very good results.

Jesús Pérez-Conde, Pierre M. Pfeuty

Vladimir I. Litvinov

Mohsen Jemaï, Peter Schuck, J. Dukelsky +1 more

Within the one-dimensional Hubbard model linear closed chains with various numbers of sites are considered in the self-consistent random phase approximation (SCRPA). Excellent results with a minimal numerical effort are obtained for $(2+4n)$-site cases, confirming earlier results with this theory for other models. However, the $4n$-site cases need further consideration. The SCRPA solves the two-site problem exactly. It therefore contains the two-electron and high-density Fermi gas limits correctly.