Abstract
We study the inhomogeneous Hubbard model with randomly distributed impurity sites with Coulomb interactions embedded in noninteracting host sites, using the dynamical mean-field theory extended to the case with site-dependent Coulomb interactions. Comparison is made with the Hubbard model which possesses the averaged effective Coulomb interactions which are proportional to impurity concentrations. For high concentrations, such a picture with the averaged effective Coulomb interactions gives reasonable results for some quantities, such as the density of states at low temperatures. At high temperatures, however, components of impurity sites and host sites are separated, leading to a clear difference from those in the homogeneous case. On the other hand, for lower concentrations, the difference appears even at low temperatures. Impurity concentration dependences of the coefficient of the specific heat linear in T and the coefficient of the resistivity square in T are different from those of the homogeneous one with the effective Coulomb interactions. In the inhomogeneous system, the high-concentration regime described by the Fermi liquid is continuously connected to the low-concentration regime which may be described by the ensemble of Kondo impurities.
Published Version
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