Exact solution of the Falicov-Kimball model with dynamical mean-field theory

TL;DR

This paper reviews the exact solution of the Falicov-Kimball model using dynamical mean-field theory, highlighting its rich phase diagram and relevance to experimental systems with correlated electrons.

Contribution

It develops the path-integral formalism for solving the Falicov-Kimball model and provides detailed expressions for its properties, serving as a benchmark for correlated electron systems.

Findings

Absence of Fermi-liquid features in the model

Rich phase diagram with metal-insulator and charge order transitions

Connections to experimental correlated electron materials

Abstract

The Falicov-Kimball model was introduced in 1969 as a statistical model for metal-insulator transitions; it includes itinerant and localized electrons that mutually interact with a local Coulomb interaction and is the simplest model of electron correlations. It can be solved exactly with dynamical mean-field theory in the limit of large spatial dimensions which provides an interesting benchmark for the physics of locally correlated systems. In this review, we develop the formalism for solving the Falicov-Kimball model from a path-integral perspective, and provide a number of expressions for single and two-particle properties. We examine many important theoretical results that show the absence of fermi-liquid features and provide a detailed description of the static and dynamic correlation functions and of transport properties. The parameter space is rich and one finds a variety of many-body features like metal-insulator transitions, classical valence fluctuating transitions, metamagnetic transitions, charge density wave order-disorder transitions, and phase separation. At the same time, a number of experimental systems have been discovered that show anomalies related to Falicov-Kimball physics [including YbInCu4, EuNi2(Si[1-x]Gex)2, NiI2 and TaxN].