Highly Correlated Particle Systems and Composite Operator Method

Abstract

Since the discovery of high Tc superconductors in cuprate oxides, physics of highly correlated electron systems has become one of the central issues in condensed matter physics. We can find many examples of highly correlated particle systems not only in electron systems, such as high Tc superconductors and transition metal oxides, but also in bosonic systems, such as alkaline atomic gases in an optical lattice and mesoscopic Josephson junction arrays. In this lecture, we illustrate several models of highly correlated particle systems of fermionic and bosonic systems, and clarify common features of these systems. Then theoretical approaches to analyze these systems will be reviewed; special emphasis is on the composite operator method, which has been developed by the present author and the Salerno group.