We use the dynamical mean-field approximation to study singularities in the self-energy and a two-particle irreducible vertex induced by the metal-insulator transition of the disordered Falicov-Kimball model. We set general conditions for the existen
ce of a critical metal-insulator transition caused by a divergence of the imaginary part of the self-energy. We calculate explicitly the critical behavior of the self-energy for the symmetric and asymmetric disorder distributions. We demonstrate that the metal-insulator transition is preceded by a pole in a two-particle irreducible vertex. We show that unlike the singularity in the self-energy the divergence in the irreducible vertex does not lead to non-analyticities in measurable physical quantities. We reveal universal features of the critical metal-insulator transition that are transferable also to the Mott-Hubbard transition in the models of the local Fermi liquid.
Mean-field theory of non-interacting disordered electron systems is widely and successfully used to describe equilibrium properties of alloys in the whole range of disorder strengths. It, however, fails to take into account effects of quantum coheren
ce and localizing back-scattering effects when applied to transport phenomena. We present an approximate scheme extending the mean-field theory for one-electron properties in that it offers a formula for the two-particle vertex and the electrical conductivity non-perturbatively including the leading-order vertex corrections in a way that the approximation remains consistent and the conductivity non-negative in all disorder regimes.
We study quantum coherence of elastically scattered lattice fermions. We calculate vertex corrections to the electrical conductivity of electrons scattered either on thermally equilibrated or statically distributed random impurities. We demonstrate t
hat the sign of the vertex corrections to the Drude conductivity is in both cases negative. Quantum coherence due to elastic back-scatterings always leads to diminution of diffusion.
The low-temperature behavior of the asymmetric single-impurity Anderson model is studied by diagrammatic methods resulting in analytically controllable approximations. We first discuss the ways one can simplify parquet equations in critical regions
of singularities in the two-particle vertex. The scale vanishing at the critical point defines the Kondo temperature at which the electron-hole correlation function saturates. We show that the Kondo temperature exists at any filling of the impurity level. A quasiparticle resonance peak in the spectral function, however, forms only in almost electron-hole symmetric situations. We relate the Kondo temperature with the width of the resonance peak. Finally we discuss the existence of satellite Hubbard bands in the spectral function.
