Electric Dipolar Susceptibility of the Anderson-Holstein Model

The temperature dependence of electric dipolar susceptibility \chi_P is discussed on the basis of the Anderson-Holstein model with the use of a numerical renormalization group (NRG) technique. Note that P is related with phonon Green's function D. In order to obtain correct temperature dependence of P at low temperatures, we propose a method to evaluate P through the Dyson equation from charge susceptibility \chi_c calculated by the NRG, in contrast to the direct NRG calculation of D. We find that the irreducible charge susceptibility estimated from \chi_c agree with the perturbation calculation, suggesting that our method works well.