V. Zlatic

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

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].

Nonequilibrium dynamical mean-field theory.

The many-body formalism for dynamical mean-field theory is extended to treat nonequilibrium problems. We illustrate how the formalism works by examining the transient decay of the oscillating current that is driven by a large electric field turned on at time t=0. We show how the Bloch oscillations are quenched by the electron-electron interactions, and how their character changes dramatically for a Mott insulator.

ANOMALOUS MAGNETIC RESPONSE OF THE SPIN-ONE-HALF FALICOV-KIMBALL MODEL

The infinite-dimensional spin one-half Falicov-Kimball model in an external magnetic field is solved exactly. We calculate the magnetic susceptibility in zero field, and the magnetization as a function of the field strength. The model shows an anomalous magnetic response from thermally excited local moments that disappear as the temperature is lowered. We describe possible real materials that may exhibit this kind of anomalous behavior.

Approximate scaling relation for the anharmonic electron-phonon problem

An approximate scaling relation is found for the transition temperature to a charge-density-wave instability in the anharmonic electron-phonon problem, which maps a wide range of interaction strengths, anharmonicities, and phonon frequencies onto a common functional form. The relation employs the wave-function renormalization parameter and is valid even for systems that are not Fermi liquids.

Kondo effect in Ce x La 1 − x Cu 2.05 Si 2 intermetallics

The magnetic susceptibility and susceptibility anisotropy of the quasibinary alloy system

VERTEX-CORRECTED PERTURBATION THEORY FOR THE ELECTRON-PHONON PROBLEM WITH NONCONSTANT DENSITY OF STATES

{\mathrm{Ce}}_{x}{\mathrm{La}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{2.05}{\mathrm{Si}}_{2}

F -electron spectral function of the Falicov-Kimball model in infinite dimensions: The half-filled case

have been studied for low concentration of Ce ions. The single-ion description is found to be valid for

Gap ratio in anharmonic charge-density-wave systems

xl~0.09.

Enhancement of thermal transport in the degenerate periodic Anderson model

The experimental results are discussed in terms of the degenerate Coqblin-Schrieffer model with a crystalline electric field splitting \ensuremath{\Delta}\ensuremath{\simeq}330 K. The properties of the model, obtained by combining the lowest-order scaling and the perturbation theory, provide a satisfactory description of the experimental data down to 30 K. The experimental results between 20 K and 2 K are explained by the exact solution of the Kondo model for an effective doublet.

Electronic thermal transport in strongly correlated multilayered nanostructures

A series of weak-coupling perturbation theories which include the lowestorder vertex corrections are applied to the attractive Holstein model in infinite dimensions. The approximations are chosen to reproduce the iterated perturbation theory in the limit of half-filling and large phonon frequency (where the Holstein model maps onto the Hubbard model). Comparison is made with quantum Monte Carlo solutions to test the accuracy of different approximation schemes.