Dynamical Mean-Field Theory - from Quantum Impurity Physics to Lattice Problems

TL;DR

This paper reviews how dynamical mean-field theory (DMFT) connects quantum impurity physics with lattice models of correlated electrons, highlighting its progress and applications in understanding phenomena like the Mott transition.

Contribution

It elucidates the relationship between impurity models and lattice models within DMFT, emphasizing the observability of impurity quantum phase transitions in lattice systems.

Findings

DMFT effectively maps lattice models to impurity problems.

Progress in understanding the Mott transition through DMFT.

Discussion on impurity quantum phase transitions in lattice models.

Abstract

Since the first investigation of the Hubbard model in the limit of infinite dimensions by Metzner and Vollhardt, dynamical mean-field theory (DMFT) has become a very powerful tool for the investigation of lattice models of correlated electrons. In DMFT the lattice model is mapped on an effective quantum impurity model in a bath which has to be determined self-consistently. This approach lead to a significant progress in our understanding of typical correlation problems such as the Mott transition; furthermore, the combination of DMFT with ab-initio methods now allows for a realistic treatment of correlated materials. The focus of these lecture notes is on the relation between quantum impurity physics and the physics of lattice models within DMFT. Issues such as the observability of impurity quantum phase transitions in the corresponding lattice models are discussed in detail.