Quantitative comparison of Anderson impurity solvers applied to transport in quantum dots

TL;DR

This paper compares various computational methods for solving the single impurity Anderson model, analyzing their accuracy and limitations in different regimes relevant to quantum dot transport.

Contribution

It provides a comprehensive comparison of EOM, NCA, OCA, and NRG methods, highlighting their strengths and weaknesses in modeling quantum dot transport phenomena.

Findings

EOM shows poor performance in Coulomb blockade regime at high temperatures.

NRG provides the most accurate results but is computationally intensive.

Some approximations fail to capture key features in certain regimes.

Abstract

We study the single impurity Anderson model (SIAM) using the equations of motion method (EOM), the non-crossing approximation (NCA), the one-crossing approximation (OCA), and Wilson's numerical renormalization group (NRG). We calculate the density of states and the linear conductance focusing on their dependence on the chemical potential and on the temperature paying special attention to the Kondo and Coulomb blockade regimes for a large range of model parameters. We report that some standard approximations based on the EOM technique display a rather unexpected poor behavior in the Coulomb blockade regime even at high temperatures. Our study offers a critical comparison between the different methods as well as a detailed compilation of the shortcomings and limitations due the approximations involved in each technique, thus allowing for a cost-benefit analysis of the different solvers that considers both numerical precision and computational performance.