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

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].

51 pages, 40 figures, submitted to Reviews of Modern Physics

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• Anomalous magnetic response of the spin-one-half Falicov-Kimball model
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• Segregation in the Falicov-Kimball model
• Charge-transfer metal-insulator transitions in the spin-one-half Falicov-Kimball model
• The Charge Ordered State from Weak to Strong Coupling
• Tuning a Josephson junction through a quantum critical point
• Falicov-Kimball model and the problem of electronic ferroelectricity
• Optical Conductivity of Ferromagnetic Semiconductors
• Optical study of the electronic phase transition of strongly correlated YbInCu_4
• Dynamical mean-field theory of a double-exchange model with diagonal disorder
• Dynamical mean-field theory of correlated hopping: A rigorous local approach
• Segregation and charge-density-wave order in the spinless Falicov-Kimball model
• Microscopic self-consistent theory of Josephson junctions including dynamical electron correlations
• Dynamical Charge Susceptibility of the Spinless Falicov-Kimball Model
• Dynamical susceptibilities in strong coupling approach
• Gap to Transition Temperature Ratio in Density Wave Ordering: a Dynamical Mean Field Study
• Saturation of electrical resistivity in metals at large temperatures
• Quantum phonons and the charge density wave transition temperature: a dynamical mean field study
• Optimizing the speed of a Josephson junction
• Inelastic X-ray scattering in correlated (Mott) insulators
• Dynamical susceptibilities in strong coupling approach: General scheme and Falikov-Kimball model
• Approximate scaling relation for the anharmonic electron-phonon problem
• Competition between phase separation and "classical" intermediate valence in an exactly solved model
• Crystal-field effects in the first-order valence transition in YbInCu4 induced by an external magnetic field
• Equivalence of the Falicov-Kimball and Brandt-Mielsch forms for the free energy of the infinite-dimensional Falicov-Kimball model
• Inelastic x-ray scattering as a probe of electronic correlations
• Gap ratio in anharmonic charge-density-wave systems
• Thermal transport in the Falicov-Kimball model

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