Ergodicity in strongly correlated systems

Abstract

We present a concise and systematic review of the ergodicity issue in strongly correlated systems. After giving a brief historical overview, we analyze the issue within the Green’s function formalism by means of the equations of motion approach. By means of this analysis, we are able to identify the primary source of non-ergodic dynamics for a generic operator as well as to give a recipe for computing unknown quantities characterizing such a behavior within the Composite Operator Method. Finally, we present examples of nontrivial strongly correlated systems where it is possible to find a non-ergodic behavior.