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arXiv:cond-mat/0702355 · Physical Review B

Hölder mean applied to Anderson localization

André M. C. Souza, Daniela Maionchi, Hans Jürgen Herrmann

Published Jul 16, 2007• 7 citations
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Abstract

The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the H\"older mean local density of states. A critical disorder strength is determined in the Anderson-Falicov-Kimball model, and the arithmetic and the geometric averages are found to be just particular means used, respectively, to detect or not the Anderson localization. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are analyzed in this perspective.

DOI
10.1103/physrevb.76.035111

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The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory using the H"older mean local density of states. A critical disorder strength is determined in the Anderson-Falicov-Kimball model, and the arithmetic and the geometric averages are found to be just particular means used, respectively, to detect or not the Anderson localization. Correlated metal, Mott insulator, and Anderson insulator phases, as well as coexistence and crossover regimes, are analyzed in this perspective.
The ground-state phase diagrams of the Falicov-Kimball model with local disorder are derived within the dynamical mean-field theory and using the geometrically averaged (``typical'') local density of states. Correlated metal, Mott insulator, and Anderson insulator phases are identified. The metal-insulator transitions are found to be continuous. The interaction and disorder compete with each other stabilizing the metallic phase against the occurring one of the insulators. The Mott and Anderson insulators are found to be continuously connected.
The phase diagram of correlated disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbor and next-nearest-neighbor hoppings. The half-filled band is analyzed in terms of the chemical potential of the system using the geometric and arithmetic averages. We also introduce the on-site energies exhibiting a long-range correlated disorder, which generates a system with similar characteristics as the one created by a random independent variable distribution. A decrease in the correlated disorder reduces the extended phase.
We investigate the stability of ``magnetic'' ordering against band-filling changes and Anderson-like disorder in the Falicov-Kimball model, within dynamical mean-field theory (DMFT). The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, allowing us to detect the localization transition. Varying the Coulomb interaction and disorder strength, we construct phase diagrams where we identify metallic and insulating regions, with or without magnetic ordering, and determine how these phases are affected by band filling.
The statistical dynamical mean field theory is used to study the metal-insulator transition in the two-dimensional Falicov-Kimball model with local disorder. Within the theory, the local density of states and its distributions are calculated. As a measure of the metal-insulator transition driven by correlation and disorder, the most probable value of the local density of states is determined. The most probable value of the local density of states is found to exhibit a discontinuity when the system crosses from extended states to localization. A phase diagram is also presented.
We derive the disorder vs doping phase diagram of the doped Hubbard model via dynamical mean-field theory combined with typical medium theory, which allows the description of both Mott (correlation driven) and Anderson (disorder driven) metal-insulator transitions. We observe a transition from a metal to an Anderson-Mott insulator for increasing disorder strength at all interactions. In the weak correlation regime and rather small doping, the Anderson-Mott insulator displays properties which are similar to the ones found at half filling. In particular, this phase is characterized by the presence of empty sites. If we further increase either the doping or the correlation, however, an Anderson-Mott phase of a different kind arises for sharply weaker disorder strength. This phase occupies the largest part of the phase diagram in the strong-correlation regime and is characterized by the absence of the empty sites.