Scaling properties of the Anderson model in the Kondo regime studied by $\sigma G \sigma W$ formalism

TL;DR

This paper investigates the Anderson model in the Kondo regime using the GW approximation within the $\sigma G \sigma W$ formalism, revealing universal scaling behavior but also limitations in capturing spin correlations and the correct Kondo scale dependence.

Contribution

It applies the GW approximation to the Anderson model in the Kondo regime and compares its scaling and Kondo scale predictions to exact solutions, highlighting both similarities and discrepancies.

Findings

GW scaling functions resemble exact solutions but differ in parameters.

GW fails to accurately describe spin correlations.

Kondo scale in GW depends algebraically on interaction strength.

Abstract

The symmetric Anderson model for a single impurity coupled to two leads is studied at strong interaction using the GW approximation within the $\sigma G \sigma W$ formalism. We find that the low energy properties show universal scaling behavior in the asymptotic regime. While the GW scaling functions are similar in form to the scaling functions known from the numerically exact solution, they are characterized by a different parameter value indicating that GW fails to describe correctly spin correlations between the impurity and lead electrons. We also compare the GW and exact Kondo scales for a broad range of the interaction strength. In contrast to the exponential behavior shown by the exact solution, the GW Kondo scale depends algebraically on the interaction strength.