Effective Models for the Anderson Impurity and the Kondo Model from Continuous Unitary Transformations

TL;DR

This paper applies continuous unitary transformations to derive convergent low-energy effective models for the Anderson impurity and Kondo models, successfully avoiding divergences and capturing the Kondo temperature and ground state properties.

Contribution

It introduces a novel application of CUTs that yields convergent effective models for impurity problems, overcoming divergence issues in traditional methods.

Findings

Derived effective models with small finite parameters at low energies.

Identified the Kondo temperature as the binding energy of a singlet ground state.

Avoided divergences typical in conventional CUT applications.

Abstract

The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent effective models. If CUTs are applied in a conventional way, diverging differential equations occur. Similar to poor man's scaling the energy scale, below which the couplings diverge, corresponds to the Kondo temperature $T_K$. We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged effective low-energy model is derived with small fnite parameters at arbitrarily small energies. The ground state corresponds to a bound singlet with a binding energy given by the Kondo temperature $T_K$.