Electric Dipolar Susceptibility of the Anderson-Holstein Model

TL;DR

This paper investigates the temperature dependence of electric dipolar susceptibility in the Anderson-Holstein model using NRG, proposing a new method to accurately evaluate susceptibility via Dyson equation and charge susceptibility.

Contribution

It introduces a novel approach to compute electric dipolar susceptibility through Dyson equation from charge susceptibility, improving low-temperature accuracy.

Findings

The proposed method aligns well with perturbation calculations.

It accurately captures the low-temperature behavior of susceptibility.

The approach enhances understanding of phonon-related properties in the model.

Abstract

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.