Spectral function of the Kondo model in high magnetic fields

TL;DR

This paper analytically calculates the spectral function of a Kondo impurity in high magnetic fields using a perturbative RG scheme, revealing decay behavior, a peak at the magnetic field, and comparing with NRG and perturbation theory.

Contribution

The paper introduces a controlled perturbative RG method to analyze the spectral function of the Kondo model at high frequencies and magnetic fields, extending understanding beyond previous approaches.

Findings

Spectral function decays as 1/ln^2(w/T_K) at large frequencies.

Pronounced peak at w=B with asymmetry in spin-resolved spectral function.

Perturbative RG controlled by 1/ln(max(w,B)/T_K).

Abstract

Using a recently developed perturbative renormalization group (RG) scheme, we calculate analytically the spectral function of a Kondo impurity for either large frequencies w or large magnetic field B and arbitrary frequencies. For large w >> max[B,T_K] the spectral function decays as 1/ln^2[ w/T_K ] with prefactors which depend on the magnetization. The spin-resolved spectral function displays a pronounced peak at w=B with a characteristic asymmetry. In a detailed comparison with results from numerical renormalization group (NRG) and bare perturbation theory in next-to-leading logarithmic order, we show that our perturbative RG scheme is controlled by the small parameter 1/ln[ max(w,B)/T_K]. Furthermore, we assess the ability of the NRG to resolve structures at finite frequencies.