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

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.