Quantum cluster theories

TLDR

Quantum cluster approaches, non‑perturbative generalized mean‑field theories, provide new perspectives for studying macroscopic correlated fermion systems and are now well established after intensive recent research. The article comparatively discusses the nature and advantages of quantum cluster techniques following a brief historical review. Quantum cluster approaches can be systematically improved, complement finite‑size simulations, and are applied to common correlated‑electron models.

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.