Non-equilibrium Scaling Properties of a Double Quantum Dot System: Comparison between Perturbative Renormalization Group and Flow Equation Approach

TL;DR

This paper compares two theoretical approaches, flow equation and perturbative renormalization group, in analyzing the non-equilibrium scaling properties of a double quantum dot system, highlighting their similarities, differences, and applicability.

Contribution

It provides a comparative analysis of flow equation and poor man's scaling methods for non-equilibrium double quantum dots, expanding understanding beyond the simpler Kondo model.

Findings

Both methods show good agreement in certain regimes.

Differences are identified in their treatment of quantum critical behavior.

The study highlights the applicability of each method to complex impurity models.

Abstract

Since the experimental realization of Kondo physics in quantum dots, its far-from-equilibrium properties have generated considerable theoretical interest. This is due to the interesting interplay of non-equilibrium physics and correlation effects in this model, which has by now been analyzed using several new theoretical methods that generalize renormalization techniques to non-equilibrium situations. While very good agreement between these methods has been found for the spin-1/2 Kondo model, it is desirable to have a better understanding of their applicability for more complicated impurity models. In this paper the differences and commons between two such approaches, namely the flow equation method out of equilibrium and the frequency-dependent poor man's scaling approach are presented for the non-equilibrium double quantum dot system. This will turn out to be a particularly suitable testing ground while being experimentally interesting in its own right. An outlook is given on the quantum critical behavior of the double quantum dot system and its accessibility with the two methods.