Scale free property and edge state of Wilson's numerical renormalization group

TL;DR

This paper explores the scale-free nature of Wilson's NRG for the Kondo problem, highlighting wavepacket basis properties, Kondo interaction effects, and the significance of edge states in low-energy physics.

Contribution

It introduces a wavepacket basis framework for Wilson's NRG, elucidates the role of Kondo interactions, and clarifies the impact of edge states on the system's low-energy behavior.

Findings

Wavepacket basis exhibits scale-free properties in Wilson's NRG.

Kondo coupling scaling analyzed within wavepacket framework.

Edge states influence the lowest energy scale in NRG.

Abstract

We discuss the scale-free property of Wilson's numerical renormalization group(NRG) for the Kondo impurity problem. The single-particle state of the effective Hamiltonian with a cutoff $\Lambda$ is described by the wavepacket basis having the scale free property; The energy scale of the system can be controlled by the lattice translation of the wavepacket basis with no reference of rescaling of the lattice space. We also analyze the role of the Kondo interaction in the context of wavepacket basis and then discuss the scaling and renormalization of the Kondo coupling. In addition, we clarify the role of the edge state in the lowest energy scale of Wilson NRG.