Singular Dynamics of Underscreened Magnetic Impurity Models

TL;DR

This paper analyzes the singular low-energy dynamics of underscreened magnetic impurity models using NRG, revealing sharp spectral features, slow convergence to fixed points, and detailed scattering properties, advancing understanding of non-Fermi liquid behavior.

Contribution

It provides a comprehensive NRG-based analysis of the low-energy fixed point and spectral properties of underscreened impurity models, highlighting their unique singular dynamics.

Findings

Spectral densities have sharp cusps at the Fermi level without divergence.

Approach to the fixed point is governed by 1/ln^2(w/T_0) terms as w -> 0.

Inelastic scattering vanishes at zero energy but more slowly than in fully screened cases.

Abstract

We give a comprehensive analysis of the singular dynamics and of the low-energy fixed point of one-channel impurity s-d models with ferromagnetic and underscreened antiferromagnetic couplings. We use the numerical renormalization group (NRG) to perform calculations at T=0. The spectral densities of the one-electron Green's functions and t-matrices are found to have very sharp cusps at the Fermi level (w=0), but do not diverge. The approach of the Fermi level is governed by terms proportional to 1/ln^2(w/T_0) as w -> 0. The scaled NRG energy levels show a slow convergence as 1/(N+C) to their fixed point values, where N is the iteration number and C is a constant dependent on the coupling J from which the low energy scale T_0 can be deduced. We calculate also the dynamical spin susceptibility, and the elastic and inelastic scattering cross-sections as a function of w. The inelastic scattering goes to zero as w-> 0, as expected for a Fermi liquid, but anomalously slowly compared to the fully screened case. We obtain the asymptotic forms for the phase shifts for elastic scattering of the quasiparticles in the high-spin and low-spin channels.