# One- and two-channel Kondo model with logarithmic Van Hove singularity: a numerical renormalization group solution

## TL;DR

This paper investigates the effects of a logarithmic Van Hove singularity on the one- and two-channel Kondo models using numerical renormalization group methods, revealing non-universal low-temperature behavior and non-Fermi-liquid characteristics.

## Contribution

It provides a detailed NRG analysis of Kondo models with Van Hove singularities, highlighting non-universal low-temperature properties and confirming results with a resonant level model.

## Key findings

- Low-temperature impurity susceptibility and entropy are non-universal and independent of coupling J.
- Two-channel case shows non-Fermi-liquid power-law behavior in local susceptibility.
- Resonant level model confirms NRG results in the strong coupling regime.

## Abstract

Simple scaling consideration and NRG solution of the one- and two-channel Kondo model in the presence of a logarithmic Van Hove singularity at the Fermi level is given. The temperature dependences of local and impurity magnetic susceptibility and impurity entropy are calculated. The low-temperature behavior of the impurity susceptibility and impurity entropy turns out to be non-universal in the Kondo sense and independent of the $s-d$ coupling $J$. The resonant level model solution in the strong coupling regime confirms the NRG results. In the two-channel case the local susceptibility demonstrates a non-Fermi-liquid power-law behavior.