Flow equations for the Anderson Hamiltonian

TL;DR

This paper develops flow equations for Hamiltonians using a continuous unitary transformation, simplifying the analysis of the Anderson Hamiltonian for dilute magnetic alloys and aligning with numerical renormalization group results.

Contribution

It introduces a simplified method to derive flow equations for Hamiltonians, providing a more straightforward approach to analyze fixed points and contributions in the Anderson model.

Findings

Flow equations produce nearly diagonal Hamiltonians.

Results agree with numerical renormalization group methods.

Simpler approach to analyzing the Anderson Hamiltonian.

Abstract

Using a continuous unitary transformation recently proposed by Wegner \cite{Wegner} together with an approximation that neglects irrelevant contributions, we obtain flow equations for Hamiltonians. These flow equations yield a diagonal or almost diagonal Hamiltonian. As an example we investigate the Anderson Hamiltonian for dilute magnetic alloys. We study the different fixed points of the flow equations and the corresponding relevant, marginal or irrelevant contributions. Our results are consistent with results obtained by a numerical renormalization group method, but our approach is considerably simpler.