Effective Equilibrium Theory of Nonequilibrium Quantum Transport

TL;DR

This paper develops an effective equilibrium approach to analyze nonequilibrium quantum transport in interacting quantum dots, providing a pedagogical framework and applying it to the Anderson model to study bias and magnetic field effects.

Contribution

It introduces a novel effective equilibrium method for nonequilibrium quantum impurity models, relating it to existing frameworks and demonstrating its application to the Anderson model.

Findings

Equivalence established between Schwinger-Keldysh and effective equilibrium observables.

Perturbative treatment of interactions capturing bias dependence.

Analysis of the Abrikosov-Suhl resonance under bias and magnetic field.

Abstract

The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [Phys. Rev. Lett. 70, 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach, and relate the Green's functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle-hole symmetric point, we investigate the fate of the Abrikosov-Suhl resonance as a function of bias voltage and magnetic field.