The Local Impurity Self Consistent Approximation (LISA) to Strongly Correlated Fermion Systems and the Limit of Infinite Dimensions

TL;DR

This paper reviews the dynamical mean-field theory (DMFT) for strongly correlated fermion systems, emphasizing its exactness in infinite dimensions, applications to the Hubbard model, and recent progress in understanding the Mott transition.

Contribution

It provides a comprehensive review of DMFT, including recent advances, applications to various models, and discusses limitations and future extensions.

Findings

Understanding of the Hubbard model and Mott transition within DMFT

Comparison of theoretical results with experiments on transition-metal oxides

Provision of numerical tools for implementing the method

Abstract

We review the dynamical mean-field theory of strongly correlated fermion systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact in the limit of large lattice coordination (or infinite spatial dimensions). This method can be used for the determination of phase diagrams and the calculation of thermodynamic properties, one-particle Green's functions, and response functions, using analytic and numerical techniques which are described. We review the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. Some applications of this method to other models are also reviewed. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are provided with this article.