Strong vs. Weak Coupling Duality and Coupling Dependence of the Kondo Temperature in the Two-Channel Kondo Model

TL;DR

This paper investigates the dependence of the Kondo temperature on coupling strength in the two-channel Kondo model, revealing a duality between weak and strong coupling regimes and providing a comprehensive mapping of $T_K(g)$.

Contribution

It introduces a unique duality mapping between small and large coupling regimes in the two-channel Kondo model, supported by numerical and analytical results.

Findings

Existence of a duality between weak and strong coupling regimes.

Quantitative agreement of $T_K(g)$ with duality predictions.

Non-monotonous $T_K(g)$ dependence with a peak at the 2CK fixed point.

Abstract

We perform numerical renormalization group (NRG) as well as analytical calculations for the two-channel Kondo model to obtain the dependence of the Kondo temperature $T_K$ on the dimensionless (bare) spin exchange coupling $g$ over the complete parameter range from $g\ll 1$ to $g\gg 1$. We show that there exists a duality between the regimes of small and large coupling. It is unique for the two-channel model and enables a mapping between the strong and the weak coupling cases via the identification $g\leftrightarrow 3/(2g)$, implying an exponential dependence of $T_K$ on $1/g$ and $g$, respectively, in the two regimes. This agrees quantitatively with our NRG calculations where we extract $T_K(g)$ over the complete parameter range and obtain a non-monotonous $T_K(g)$ dependence, strongly peaked at the 2CK fixed point coupling $g^*$. These results may be relevant for resolving the long-standing puzzle within the 2CK interpretation of certain random defect systems, why no broad distribution of $T_K$ is observed in those systems.