The Strong Coupling Fixed-Point Revisited

TL;DR

This paper revisits the strong coupling fixed point of impurity models, using a combined numerical renormalization group and renormalized perturbation theory approach to accurately analyze low-temperature behavior and magnetic field effects.

Contribution

It extends the renormalized perturbation theory framework to include magnetic field dependence, enabling precise low-temperature predictions for impurity models under magnetic fields.

Findings

Effective calculation of low-temperature impurity behavior.

Extension of RPT to magnetic field dependence.

Accurate modeling of magnetic field effects on quasiparticles.

Abstract

In recent work we have shown that the Fermi liquid aspects of the strong coupling fixed point of the s-d and Anderson models can brought out more clearly by interpreting the fixed point as a renormalized Anderson model, characterized by a renormalized level $\tilde\epsilon_d$, resonance width, $\tilde\Delta$, and interaction $\tilde U$, and a simple prescription for their calculation was given using the numerical renormalization group (NRG). These three parameters completely specify a renormalized perturbation theory (RPT) which leads to exact expressions for the low temperature behaviour. Using a combination of the two techniques, NRG to determine $\tilde\epsilon_d$, $\tilde\Delta$, and $\tilde U$, and then substituting these in the RPT expressions gives a very efficient and accurate way of calculating the low temperature behaviour of the impurity as it avoids the necessity of subtracting out the conduction electron component. Here we extend this approach to an Anderson model in a magnetic field, so that $\tilde\epsilon_d$, $\tilde\Delta$, and $\tilde U$ become dependent on the magnetic field. The de-renormalization of the renormalized quasiparticles can then be followed as the magnetic field strength is increased. Using these running coupling constants in a RPT calculation we derive an expression for the low temperature conductivity for arbitrary magnetic field strength.