Electron--electron Interactions in Disordered Metals: Keldysh Formalism

TL;DR

This paper introduces a new field theory formalism using the Keldysh approach for disordered interacting electrons, enabling non-equilibrium analysis and automatically handling divergences, with implications for understanding quantum fluctuations and conductivity corrections.

Contribution

It develops a Keldysh-based field theory formalism as an alternative to replica methods for disordered electron liquids, incorporating non-equilibrium effects and divergence cancellations.

Findings

Derives a non-perturbative expression for the single particle density of states.

Shows that Altshuler-Aronov corrections arise from quantum fluctuations.

Separates phase effects from quasi-particle dynamics in the formalism.

Abstract

We develop a field theory formalism for the disordered interacting electron liquid in the dynamical Keldysh formulation. This formalism is an alternative to the previously used replica technique. In addition it naturally allows for the treatment of non-equilibrium effects. Employing the gauge invariance of the theory and carefully choosing the saddle point in the $Q$-matrix manifold, we separate purely phase effects of the fluctuating potential from the ones that change quasi-particle dynamics. As a result, the cancellation of super-divergent diagrams (double logarithms in d=2) is automatically build in the formalism. As a byproduct we derive a non--perturbative expression for the single particle density of states. The remaining low-energy sigma--model describes the quantum fluctuations of the electron distribution function. Its saddle point equation appears to be the quantum kinetic equation with an appropriate collision integral along with collisionless terms. Altshuler-Aronov corrections to conductivity are shown to arise from the one-loop quantum fluctuation effects.