Comment on "Twofold Advance in the Theoretical Understanding of Far-From-Equilibrium Properties of Interacting Nanostructures"

TL;DR

This paper challenges the notion that negative differential conductance in the interacting resonant level model is inherently nonperturbative, demonstrating it can be explained and calculated using simple physical arguments and perturbation theory.

Contribution

It provides a perturbative explanation for negative differential conductance in the IRLM, countering previous claims of its nonperturbative nature.

Findings

NDC can be explained by simple physical arguments.

Perturbation theory can be used to calculate NDC in certain conditions.

Supports the idea that NDC is not necessarily a nonperturbative phenomenon.

Abstract

Boulat, Saleur and Schmitteckert (BSS) reported results on the full $I-V$ characteristics of the interacting resonant level model (IRLM) exhibiting region with unexpected negative differential conductance (NDC). Using time-dependent density matrix renormalization group complemented with the exact solution performed at a special point (the self-dual point) in the parameter space BSS have shown that at nonzero Coulomb interaction $U$ the current flowing through the impurity level (IL) exhibits a power-law asymptotics as a function of large applied bias voltage. Similar conclusion was earlier reached by Doyon. Even though their results are solid and supported by both analytic and numeric arguments, BSS concluded that "the NDC at large voltage seems a truly nonperturbative behavior, with unclear physical origin". On the contrary, the remarkable physics of NDC can be explained by simple physical arguments and, as we shall show in this Comment, in certain circumstances can be calculated in the framework of perturbation theory.