Ergodicity in Strongly Correlated Systems

TL;DR

This paper reviews the concept of ergodicity in strongly correlated systems, analyzing its origins and manifestations using Green's function formalism, and provides methods to identify and compute non-ergodic behavior with practical examples.

Contribution

It offers a systematic analysis of ergodicity issues in strongly correlated systems using Green's function formalism and introduces a recipe for computing non-ergodic behavior.

Findings

Identifies primary sources of non-ergodic dynamics.

Provides a method to compute non-ergodic quantities.

Examples of non-ergodic behavior in complex systems.

Abstract

We present a concise, but 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 individuate the primary source of non-ergodic dynamics for a generic operator and also to give a recipe to compute unknown quantities characterizing such a behavior within the Composite Operator Method. Finally, we present examples of non-trivial strongly correlated systems where it is possible to find a non-ergodic behavior.