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

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 $T_K$.

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Cited by in corpus (8)

• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• High-frequency asymptotics of the vertex function: diagrammatic parametrization and algorithmic implementation
• In-Medium Similarity Renormalization Group for Closed and Open-Shell Nuclei
• In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
• Nuclear Structure from the In-Medium Similarity Renormalization Group
• Stable Unitary Integrators for the Numerical Implementation of Continuous Unitary Transformations
• Crystal fields and Kondo effect: new results for the magnetic susceptibility
• Poor man's scaling and Lie algebras