Spin and Charge Dynamics in a Renormalised Perturbation Theory

TL;DR

This paper develops a renormalised perturbation theory to accurately calculate spin and charge susceptibilities in a strongly correlated impurity model, matching numerical results across all frequencies and magnetic fields.

Contribution

It introduces a method to compute dynamical susceptibilities using renormalised parameters derived from NRG, providing a comprehensive and accurate description beyond low frequencies.

Findings

RPT matches NRG results across all frequencies

Accurate spin dynamics in magnetic fields using field-dependent parameters

Susceptibilities satisfy the Korringa-Shiba relation

Abstract

We calculate the spin and charge dynamical susceptibilities of a strongly correlated impurity model in a renormalised perturbation theory. The irreducible for vertices for the quasiparticle scattering are deduced from the renormalised parameters, which have been calculated by fitting of the low-lying levels of a numerical renormalisation group (NRG) calculation to those of an effective Anderson model. The susceptibilities are asymptotically exact in the low frequency limit and satisfy the Korringa-Shiba relation. By comparing the results with those calculated from a direct NRG calculation, we show that the renormalised perturbation theory (RPT) description gives a very good description of spin dynamics for all values of the local interaction U, not only at low frequencies but over the whole relevant frequency range. In the presence of a magnetic field the approach can be generalised using field dependent renormalised parameters to calculate the transverse and parallel spin dynamic susceptibilities. The RPT results give accurate results for the spin dynamics over the whole frequency range and for all values of the magnetic field.