Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data

TL;DR

This paper compares analytical and quantum Monte Carlo methods to analyze the spectral function of the nonequilibrium Anderson impurity model, revealing how voltage influences the Kondo effect and spectral features.

Contribution

It provides explicit formulas for the nonequilibrium self-energy and demonstrates the agreement between perturbation theory and Monte Carlo data up to moderate interaction strengths.

Findings

Perturbation theory matches Monte Carlo data for U/Γ up to 2.

Finite voltage acts as an effective temperature suppressing the Kondo effect.

No resonance splitting occurs at voltages above the Kondo temperature.

Abstract

We analyze the spectral function of the single-impurity two-terminal Anderson model at finite voltage using the recently developed diagrammatic quantum Monte Carlo technique as well as perturbation theory. In the (particle-hole-)symmetric case we find an excellent agreement of the numerical data with the perturbative results of second order up to interaction strengths $U/\Gamma \approx 2$, where $\Gamma$ is the transparency of the impurity-electrode interface. The analytical results are obtained in form of the nonequilibrium self-energy for which we present explicit formulas in the closed form at arbitrary bias voltage. We observe an increase of the spectral density around zero energy brought about by the Kondo effect. Our analysis suggests that a finite applied voltage $V$ acts as an effective temperature of the system. We conclude that at voltages significantly larger than the equilibrium Kondo temperature there is a complete suppression of the Kondo effect and no resonance splitting can be observed. We confirm this scenario by comparison of the numerical data with the perturbative results.