Double Occupancy and Magnetic Susceptibility of the Anderson Impurity Model out of Equilibrium

TL;DR

This paper compares various numerical methods to study how double occupancy and magnetic susceptibility in the Anderson impurity model behave under bias voltage, revealing different sensitivities to the Kondo effect and discrepancies among methods.

Contribution

It provides a comparative analysis of MV-QMC, SNRG, and RT-QMC approaches for out-of-equilibrium Anderson impurity models, highlighting their agreements and differences.

Findings

Magnetic susceptibility results are consistent across methods in the Kondo limit.

Double occupancy shows different behavior and is less directly related to the Kondo scale.

All methods differ in predicting charge fluctuations in strongly interacting regimes out of equilibrium.

Abstract

We use different numerical approaches to calculate the double occupancy and mag- netic susceptibility as a function of a bias voltage in an Anderson impurity model. Specifically, we compare results from the Matsubara-voltage quantum Monte-Carlo approach (MV-QMC), the scattering-states numerical renormalization group (SNRG), and real-time quantum Monte-Carlo (RT-QMC), covering Coulomb repulsions ranging from the weak-coupling well into the strong- coupling regime. We observe a distinctly different behavior of the double occupancy and the magnetic response. The former measures charge fluctuations and thus only indirectly exhibits the Kondo scale, while the latter exhibits structures on the scale of the equilibrium Kondo tempera- ture. The Matsubara-voltage approach and the scattering-states numerical renormalization group yield consistent values for the magnetic susceptibility in the Kondo limit. On the other hand, all three numerical methods produce different results for the behavior of charge fluctuations in strongly interacting dots out of equilibrium.