In this work, we study the Anderson-Falicov-Kimball model within the dynamical mean field theory for the Bethe lattice, restricting our analysis to the nonmagnetic case. The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, since only the latter can detect localization in the absence of an energy gap. Varying the strengths of Coulomb interaction and disorder at zero temperature, we construct phase diagrams for this model, where we distinguish spectral regions with localized states, with extended states, or with a correlation-induced gap. With this, we identify metal-insulator transitions driven by correlation and disorder, as well as the competition between these effects. This is done for various band fillings, since our main interest here is to study how the variation of the electron density affects the phase diagrams previously obtained for half-filling. The picture revealed by the density of states is further checked by evaluating the static and dynamic conductivities, including temperature effects.
In this work, we study the Anderson-Falicov-Kimball model within the dynamical mean field theory for the Bethe lattice, restricting our analysis to the nonmagnetic case. The one-particle density of states is obtained by both arithmetic and geometric averages over disorder, since only the latter can detect localization in the absence of an energy gap. Varying the strengths of Coulomb interaction and disorder at zero temperature, we construct phase diagrams for this model, where we distinguish spectral regions with localized states, with extended states, or with a correlation-induced gap. With this, we identify metal-insulator transitions driven by correlation and disorder, as well as the competition between these effects. This is done for various band fillings, since our main interest here is to study how the variation of the electron density affects the phase diagrams previously obtained for half-filling. The picture revealed by the density of states is further checked by evaluating the static and dynamic conductivities, including temperature effects.
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 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 effects of Coulomb disorder on the half-filled ionic Hubbard model within the framework of dynamical mean-field theory (DMFT), using the equation-of-motion method as the impurity solver, combined with typical medium theory (TMT). In contrast to conventional disordered Hubbard models, the ionic Hubbard model contains a staggered ionic potential that introduces additional competition between band-insulating and correlation-driven insulating tendencies. We analyze how this ionic potential modifies the electronic phases induced by Coulomb disorder through the arithmetic and geometric averages of the local density of states. In the absence of disorder, the system exhibits metallic (M), Mott-insulating (MI), and band-insulating (BI) phases. When Coulomb disorder is introduced, Anderson-insulating (AI) behavior and localized states (LS) inside the Mott gap are also observed. In particular, the LS regime appears between the metallic and Mott-insulating phases at small ionic potentials, whereas the AI regime develops for sufficiently large values of the Coulomb interaction and ionic potential. Our results show that the interplay between ionic potential, electron correlation, and disorder substantially influences the localization behavior and insulating characteristics of the ionic Hubbard model.
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.
Abstract We study the half-filled Hubbard model with Anderson and Coulomb disorder by mean of dynamical mean field theory using the geometrically averaged local density of states. The paramagnetic phase diagram of the model as a function of the Coulomb interaction and Anderson disorder strength is obtained. The spectral phase diagrams of the ground states for the model are also constructed and discussed. We show that in the intermediate and strong interaction regimes, the Coulomb disorder leads the metallic and Mott insulator phase regions shrink, while the Anderson insulator region is enlarged.
We analyze the transformation from insulator to metal induced by thermal fluctuations within the Falicov-Kimball model. Using the dynamic mean field theory (DMFT) formalism on the Bethe lattice we find rigorously the temperature dependent density of states (DOS) at half filling in the limit of high dimensions. At zero temperature (T=0) the system is ordered to form the checkerboard pattern and the DOS has the gap $\ensuremath{\Delta}$ at the Fermi level ${\ensuremath{\varepsilon}}_{F}=0$, which is proportional to the interaction constant U. With an increase of T the DOS evolves in various ways that depend on U. For U>Ucr the gap persists for any T (then $\ensuremath{\Delta}>0$), so the system is always an insulator. However, if U<Ucr, two additional subbands develop inside the gap. They become wider with increasing T and at a certain U-dependent temperature TMI they join with each other at ${\ensuremath{\varepsilon}}_{F}$. Since above TMI the DOS is positive at ${\ensuremath{\varepsilon}}_{F}$, we interpret TMI as the transformation temperature from insulator to metal. It appears that TMI approaches the order-disorder phase transition temperature ${T}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{DO}}$ when U is close to 0 or Ucr, but TMI is substantially lower than ${T}_{\mathrm{O}\text{\ensuremath{-}}\mathrm{DO}}$ for intermediate values of U. Moreover, using an analytical formula we show that TMI=0 at U=2<Ucr, so we prove that the quantum critical point exists for the ordered metal at (T=0,U=2). Having calculated the temperature dependent DOS we study thermodynamic properties of the system starting from its free energy F. Then we find how the order parameter d and the gap $\ensuremath{\Delta}$ change with T and we construct the phase diagram in the variables T and U, where we display regions of stability of four different phases: ordered insulator, ordered metal, disordered insulator, and disordered metal. Finally, we use a low temperature expansion to demonstrate the existence of a nonzero DOS at a characteristic value of U on a general bipartite lattice.