V. Janis

COMPREHENSIVE MEAN FIELD THEORY FOR THE HUBBARD MODEL

We derive an exact expression for the grand potential of the Hubbard model in d=∞ dimensions. By simplifying the energy transfer between up and down spins we obtain a comprehensive mean-field theory for this model. It is (i) thermodynamically consistent in the entire range of input parameters, (ii) conserving and, (iii) exact in several non-trivial limits, e. g. in the free (U→0), atomic (t→0) and Heisenberg (U≫t, n=1) limit.

Parquet approach to nonlocal vertex functions and electrical conductivity of disordered electrons

A diagrammatic technique for two-particle vertex functions is used to describe systematically the influence of spatial quantum coherence and backscattering effects on transport properties of noninteracting electrons in a random potential. In analogy with many-body theory we construct parquet equations for topologically distinct nonlocal irreducible vertex functions into which the local one-particle propagator and two-particle vertex of the coherent-potential approximation (CPA) enter as input. To complete the two-particle parquet equations we use an integral form of the Ward identity and determine the one-particle self-energy from the known irreducible vertex. In this way a conserving approximation with (Herglotz) analytic averaged Green functions is obtained. We use the limit of high spatial dimensions to demonstrate how nonlocal corrections to the

Density and current response functions in strongly disordered electron systems: Diffusion, electrical conductivity and Einstein relation

d=\ensuremath{\infty}

Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads

(CPA) solution emerge. The general parquet construction is applied to the calculation of vertex corrections to the electrical conductivity. With the aid of the high-dimensional asymptotics of the nonlocal irreducible vertex in the electron-hole scattering channel we derive a mean-field approximation for the conductivity with vertex corrections. The impact of vertex corrections onto the electronic transport is assessed quantitatively within the proposed mean-field description on a binary alloy.

STABILITY OF SELF-CONSISTENT SOLUTIONS FOR THE HUBBARD MODEL AT INTERMEDIATE AND STRONG COUPLING

Abstract.We study noninteracting quantum charged particles (electron gas) subject to a strong random potential and perturbed by a weak classical electromagnetic field. We examine consequences of gauge invariance and charge conservation in the space of Bloch waves. We use two specific forms of the Ward identity between the one- and two-particle averaged Green functions to establish exact relations between the density and current response functions. In particular, we find precise conditions under which we can extract the current-current from the density-density correlation functions and vice versa. We use these results to prove a formula relating the density response and the electrical conductivity in strongly disordered systems. We introduce quantum diffusion as a response function that reduces to the diffusion constant in the static limit. We then derive Fick’s law, a quantum version of the Einstein relation and prove the existence of the diffusion pole in the quasistatic limit of the zero-temperature electron-hole correlation function. We show that the electrical conductivity controls the long-range spatial fluctuations of the electron-hole correlation function only in the static limit.

Kondo behavior in the asymmetric Anderson model: Analytic approach

Self-consistent perturbation expansion up to the second order in the interaction strength is used to study a single-level quantum dot with local Coulomb repulsion attached asymmetrically to two generally different superconducting leads. At zero temperature and wide range of other parameters the spin-symmetric version of the expansion yields excellent results for the position of the

The Hubbard model at intermediate coupling: renormalization of the interaction strength

0-\pi

Equilibrium state of the mean-field Potts glass

impurity quantum phase transition boundary and Josephson current together with the energy of Andreev bound states in the

Analytic impurity solver with Kondo strong-coupling asymptotics

0

Mean-field theories for disordered electrons: Diffusion pole and Anderson localization

-phase as confirmed by numerical calculations using the Numerical Renormalisation Group method. We analytically prove that the method is charge-conserving as well as thermodynamically consistent. Explicit formulas for the position of the