Ground State Properties of Anderson Impurity in a Gapless Host

TL;DR

This paper investigates the ground state of a large-U Anderson impurity in a gapless host using Bethe ansatz, revealing universal spin screening but nonuniversal impurity occupancy behavior that clarifies previous conflicting results.

Contribution

It provides an exact Bethe ansatz analysis of the Anderson impurity in a gapless host, highlighting novel occupancy features and explaining the absence of Kondo screening in earlier scaling studies.

Findings

Impurity spin is screened at all parameters.

Impurity occupancy shows nonuniversal behavior.

Kondo screening may be absent or only at large coupling.

Abstract

Using the Bethe ansatz method, we study the ground state properties of a $U\to\infty$ Anderson impurity in a ``gapless'' host, where a density of band states vanishes at the Fermi level $\epsilon_F$ as $|\epsilon-\epsilon_F|$. As in metals, the impurity spin is proven to be screened at arbitrary parameters of the system. However, the impurity occupancy as a function of the bare impurity energy is shown to acquire novel qualitative features which demonstrate a nonuniversal behavior of the system. The latter explains why the Kondo screening is absent (or exists only at quite a large electron-impurity coupling) in earlier studies based on scaling arguments.