Scaling Law for a Magnetic Impurity Model with Two-Body Hybridization

TL;DR

This paper investigates a magnetic impurity model with two-body hybridization, emphasizing its importance for accurate scaling theory at large band widths, and maps the phase transition boundary between Fermi and non-Fermi liquid states.

Contribution

It introduces the inclusion of two-body hybridization in the scaling theory for magnetic impurity models, extending the validity of the theory to larger band widths.

Findings

Two-body hybridization is crucial for valid scaling at large band widths.

Mapped the phase boundary between Fermi and non-Fermi liquid states.

Demonstrated the model's behavior using poor man's scaling and generalized theories.

Abstract

We consider a magnetic impurity coupled to the hybridizing and screening channels of a conduction band. The model is solved in the framework of poor man's scaling and Cardy's generalized theories. We point out that it is important to include a two-body hybridization if the scaling theory is to be valid for the band width larger than $U$. We map out the boundary of the Fermi-non-Fermi liquid phase transition as a function of the model parameters.