Current-density functional for disordered systems

TL;DR

This paper develops a non-perturbative current-density functional approach for disordered systems, deriving an evolution equation that describes how vertex functions depend on disorder and interactions, and applies it to compute conductivity.

Contribution

It introduces a functional generalization of the Callan-Symanzik equation for disordered systems, providing a new method to analyze disorder effects non-perturbatively.

Findings

Conductivity vanishes beyond a certain impurity threshold.

The evolution equation describes dependence on disorder strength.

Numerical solutions illustrate the static limit behavior.

Abstract

The effective action for the current and density is shown to satisfy an evolution equation, the functional generalization of Callan-Symanzik equation. The solution describes the dependence of the one-particle irreducible vertex functions on the strength of the quenched disorder and the annealed Coulomb interaction. The result is non-perturbative, no small parameter is assumed. The a.c. conductivity is obtained by the numerical solution of the evolution equation on finite lattices in the absence of the Coulomb interaction. The static limit is performed and the conductivity is found to be vanishing beyond a certain threshold of the impurity strength.