Mott-Hubbard transition versus Anderson localization in correlated electron systems with disorder

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the geometrically averaged ("typical") local density of states. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are identified. The Mott and Anderson insulators are found to be continuously connected.     

New dynamical mean-field dynamo theory and closure approach

We develop a new nonlinear mean field dynamo theory that couples field growth to the time evolution of the magnetic helicity and the turbulent electromotive force, E. We show that the difference between kinetic and current helicities emerges naturally as the growth driver when the time derivative of E is coupled into the theory. The solutions predict significant field growth in a kinematic phase and a saturation rate/strength that is magnetic Reynolds number dependent/independent in agreement with numerical simulations. The amplitude of early time oscillations provides a diagnostic for the closure.     

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.     

Finite-temperature magnetism of transition metals: an ab initio dynamical mean-field theory

We present an ab initio quantum theory of the finite-temperature magnetism of iron and nickel. A recently developed technique which combines dynamical mean-field theory with realistic electronic structure methods successfully describes the many-body features of the one electron spectra and the observed magnetic moments below and above the Curie temperature.     

Self-energy-functional approach: Analytical results and the Mott-Hubbard transition

The self-energy-functional approach proposed recently is applied to the single-band Hubbard model at half-filling to study the Mott-Hubbard metal-insulator transition within the most simple but non-trivial approximation. This leads to a mean-field approach which is interesting conceptually: Trial self-energies from a two-site single-impurity Anderson model are used to evaluate an exact and general variational principle. While this restriction of the domain of the functional represents a strong approximation, the approach is still thermodynamically consistent by construction and represents a conceptual improvement of the linearized DMFT which has been suggested previously as a handy approach to study the critical regime close to the transition. It turns out that the two-site approximation is able to reproduce the complete (zero and finite-temperature) phase diagram for the Mott transition. For the critical point at T = 0, the entire calculation can be done analytically. This calculation elucidates different general aspects of the self-energy-functional theory. Furthermore, it is shown how to deal with a number of technical difficulties which appear when the self-energy functional is evaluated in practice.Received: 3 November 2003, Published online: 23 December 2003PACS: 71.10.-w Theories and models of many-electron systems - 71.15.-m Methods of electronic structure calculations - 71.30. + h Metal-insulator transitions and other electronic transitions     

Mott transition in the asymmetric Hubbard model at half-filling within dynamical mean-field theory

The asymmetric Hubbard model with hopping integrals dependent on an electron spin (particle sort) is studied using an approximate analytic method within the dynamical mean-field theory. The equations of motion for Hubbard operators followed by projecting and different-time decoupling are used for solving the single-site problem. Particle spectra are investigated at half-filling within various approximations (Hubbard-I, alloy-analogy and a generalization of the Hubbard-III approximation). At half-filling these approximations can describe only continuous gap opening in the spectrum. The approach is used to describe the system between two limit cases (the Falicov-Kimball model and the standard Hubbard model) with continuous transition where U_c is dependent on the value of hopping parameters of different particles.     

Electronic coherence in delta-Pu: a dynamical mean-field theory study

A combination of density functional theory and the dynamical mean-field theory (DMFT) is used to calculate the magnetic susceptibility, heat capacity, and the temperature dependence of the valence band photoemission spectra for delta-Pu. We predict that delta-Pu has a Pauli-like magnetic susceptibility near ambient temperature, as in experiment, indicating that electronic coherence causes the absence of local moments. Additionally, we show that volume expansion causes a crossover from incoherent to coherent electronic behavior at increasingly lower temperatures.     

Microscopic mean-field theory of the jamming transition

Dense particle packings acquire rigidity through a nonequilibrium jamming transition commonly observed in materials from emulsions to sandpiles. We describe athermal packings and their observed geometric phase transitions by using equilibrium statistical mechanics and develop a fully microscopic, mean-field theory of the jamming transition for soft repulsive spherical particles. We derive analytically some of the scaling laws and exponents characterizing the transition and obtain new predictions for microscopic correlation functions of jammed states that are amenable to experimental verifications and whose accuracy we confirm by using computer simulations.     

Dielectric breakdown of Mott insulators in dynamical mean-field theory

Using nonequilibrium dynamical mean-field theory, we compute the time evolution of the current in a Mott insulator after a strong electric field is turned on. We observe the formation of a quasistationary state in which the current is almost time independent although the system is constantly excited. At moderately strong fields this state is stable for quite long times. The stationary current exhibits a threshold behavior as a function of the field, in which the threshold increases with the Coulomb interaction and vanishes as the metal-insulator transition is approached.     

Semiclassical theory of the Anderson transition

We study analytically the metal-insulator transition in a disordered conductor by combining the self-consistent theory of localization with the one parameter scaling theory. We provide explicit expressions of the critical exponents and the critical disorder as a function of the spatial dimensionality d. The critical exponent nu controlling the divergence of the localization length at the transition is found to be nu=1/2+1/d-2 thus confirming that the upper critical dimension is infinity. Level statistics are investigated in detail. We show that the two level correlation function decays exponentially and the number variance is linear with a slope which is an increasing function of the spatial dimensionality. Our analytical findings are in agreement with previous numerical results.     

First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory

We propose a dynamical mean-field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean-field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional "LDA+DMFT," such as Hubbard interaction parameters and double-counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.     

Nonlinear transport through strongly correlated two-terminal heterostructures: a dynamical mean-field approach

The dynamical-mean-field method is applied to investigate the transport properties of heterostructures consisting of a strongly correlated electron system connected to metallic leads. The spectral function inside the correlated region is sensitive to the change of the interaction strength and bias voltage. Because of this sensitivity, current vs voltage characteristics of such heterostructures are rather nonlinear regardless of the detail of the potential profile inside the correlated region. The electronic properties such as the double occupancy are also changed by the bias voltage.     

Anderson localization and superconducting transition temperature in two-dimensional systems

Effects of the Anderson localization on superconducting transition temperature T_c are examined by calculating a two-electron propagator K rigorously up to 0[(?_Fτ₀)^?1ln(Tτ₀)], where τ₀ is the electron life time due to impurity scattering and ?_F the Fermi energy. The results show that in K the pair-breaking terms cancel out among themselves exactly and the remaining terms which contribute to the correction to the density of states and to the renormalization of electron-electron interaction by impurity scattering lead to the changes in T_c of 0[{ln(Tτ₀)}²] and of 0[{ln(Tτ₀)}³], respectively.     

A self-consistent approach to localization transition

The Anderson transition is investigated using a self-consistent approximation in analogy with mean-field approximations in classical spin systems. Mobility edge trajectories in a three-dimensional disordered system with various distributions of the site energies are obtained. The present results are qualitatively in good agreement with the results obtained by using the finite-size scaling method.     

Time-dependent density-functional theory meets dynamical mean-field theory: real-time dynamics for the 3D Hubbard model

We introduce a new class of exchange-correlation potentials for a static and time-dependent density-functional theory of strongly correlated systems in 3D. The potentials are obtained via dynamical mean-field theory and, for strong enough interactions, exhibit a discontinuity at half-filling density, a signature of the Mott transition. For time-dependent perturbations, the dynamics is described in the adiabatic local density approximation. Results from the new scheme compare very favorably to exact ones in clusters. As an application, we study Bloch oscillations in the 3D Hubbard model.