Quantum Cluster Theories

TL;DR

Quantum cluster theories are advanced, non-perturbative methods that provide systematic, thermodynamic-limit insights into correlated fermion systems, complementing finite size simulations and improving understanding of complex electron behaviors.

Contribution

This paper reviews the development, advantages, and applications of quantum cluster approaches in studying correlated electron systems, highlighting their systematic improvements and complementary nature.

Findings

Quantum cluster methods are non-perturbative and in the thermodynamic limit.

They can be systematically improved for better accuracy.

Applications demonstrate their effectiveness in modeling correlated electron systems.

Abstract

Quantum cluster approaches offer new perspectives to study the complexities of macroscopic correlated fermion systems. These approaches can be understood as generalized mean-field theories. Quantum cluster approaches are non-perturbative and are always in the thermodynamic limit. Their quality can be systematically improved, and they provide complementary information to finite size simulations. They have been studied intensively in recent years and are now well established. After a brief historical review, this article comparatively discusses the nature and advantages of these cluster techniques. Applications to common models of correlated electron systems are reviewed.