Variational approach to transport in quantum dots

TL;DR

This paper introduces a variational principle for modeling nonequilibrium transport in quantum dots, applying it to the Anderson impurity model, and demonstrating qualitative agreement with experimental observations.

Contribution

It develops a new variational approach for nonequilibrium steady states in quantum impurity systems, specifically applying Gutzwiller's variational space to the Anderson model.

Findings

Qualitative agreement with quantum dot behavior at certain biases

Simple and flexible variational methods for complex systems

Formal definition of a variational principle in nonequilibrium

Abstract

We have derived a variational principle that defines the nonequilibrium steady-state transport across a correlated impurity mimicking, e.g., a quantum dot coupled to biased leads. This variational principle has been specialized to a Gutzwiller's variational space, and applied to the study of the simple single-orbital Anderson impurity model at half filling, finding a good qualitative accord with the observed behavior in quantum dots for the expected regime of values of the bias. Beyond the purely theoretical interest in the formal definition of a variational principle in a nonequilibrium problem, the particular methods proposed have the important advantage to be simple and flexible enough to deal with more complicated systems and variational spaces.