The Kondo effect in the presence of Van Hove singularities: A numerical renormalization group study

TL;DR

This study uses numerical renormalization group methods to explore how Van Hove singularities affect the Kondo effect on a square lattice, revealing complex thermodynamic behavior and deviations from Fermi-liquid theory.

Contribution

It provides a detailed numerical analysis of the Kondo effect with Van Hove singularities, highlighting crossover behaviors and low-temperature properties.

Findings

Inverse logarithm of Kondo temperature shows crossover behavior.

Low-temperature susceptibility and specific heat deviate from Fermi-liquid predictions.

Wilson ratio is calculated for different parameters.

Abstract

A numerical renormalization group (NRG) investigation of the one-centre $t-t'$ Kondo problem is performed for the square lattice with account of logarithmic Van Hove singularities (VHS) in the electron density of states. The magnetic susceptibility, entropy and specific heat are calculated. The temperature dependences of the thermodynamic properties in the presence of VHS turn out to be non-trivial. For finite $t'$ inverse logarithm of the corresponding Kondo temperature $T_K$ demonstrates a crossover from the square-root to standard linear dependence on the $s-d$ exchange coupling. The low-temperature behavior of magnetic susceptibility and linear specific heat are investigated, and the Wilson ratio is obtained. For $t' -> 0$ the Fermi-liquid behavior is broken.