Perturbation approach for the Kondo Hamiltonian.

Abstract

The bosonized Kondo Hamiltonian is obtained by comparing the long-time limit of the reduced grand partition function for the impurity spin. We analyze this bosonized Kondo Hamiltonian at zero temperature and derive an effective Hamiltonian describing the effective interaction between the conduction electrons via an impurity-spin scattering. The infrared divergences encountered in the conventional perturbation theory are caused by this growth effective coupling at the low-energy limit. With the Bogoliubov transformation, we have developed a perturbation approach for this effective Hamiltonian and investigated the nontrivial ferromagnetic-antiferromagnetic crossover of the impurity spin. The critical condition derived here is in agreement with the renormalization-group numerical result. In particular, the ground-state wave function and its excitation spectrum of the conduction electrons are also obtained. Moreover, this effective Hamiltonian may be mapped onto a modified quantum sine-Gordon model. Paralleling the renormalization-group theory of the quantum sine-Gordon model, we straightforwardly reproduce previous results and derive the higher-order terms and a new universal correction in the flow equations.