Renormalized Parameters for Impurity Models

TL;DR

This paper demonstrates that diverse impurity systems at low energy can be effectively described by a single renormalized Anderson model with three parameters, capturing various interactions including phonons and Falikov-Kimball terms.

Contribution

It introduces a unified renormalized Anderson model with three parameters that accurately describes low energy impurity systems with different interactions.

Findings

Renormalized parameters are computed for various impurity models.

Interaction sign change identified as a function of electron-phonon coupling.

Low energy behavior approximates a shifted impurity level in Falikov-Kimball models.

Abstract

We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level $\tilde\epsilon_d$, an effective hybridization $\tilde V$, and a quasiparticle interaction $\tilde U$. The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.