Ruprecht-Karls-Universität Heidelberg
University of HeidelbergFaculty of Physics and AstronomyInstitut of Theoretical PhysicsAndreas MielkeAndreas Mielkeemail

Andreas Mielke
Institut for Theoretical Physics
Ruprecht-Karls University
Philosophenweg 19
D-69120 Heidelberg
Tel.: ++49 6221 549431 (Secretary)
Fax: ++49 6221 549331

Stefan Kehrein, Andreas Mielke: Theory of the Anderson impurity model: The Schrieffer-Wolff transformation re-examined
Ann. Physics (NY)252, 1-32 (1996) .

Archiv: cond-mat/9510145


We apply the method of infinitesimal unitary transformations recently introduced by Wegner to the Anderson single impurity model. It is demonstrated that this method provides a good approximation scheme for all values of the on-site interaction $U$, it becomes exact for $U=0$. We are able to treat an arbitrary density of states, the only restriction being that the hybridization should not be the largest parameter in the system. Our approach constitutes a consistent framework to derive various results usually obtained by either perturbative renormalization in an expansion in the hybridization Anderson's 'poor man's' scaling approach or the Schrieffer-Wolff unitary transformation. In contrast to the Schrieffer-Wolff result we find the correct high-energy cutoff and avoid singularities in the induced couplings. An important characteristic of our method as compared to the 'poor man's' scaling approach is that we continuously decouple modes from the impurity that have a large energy difference from the impurity orbital energies. In the usual scaling approach this criterion is provided by the energy difference from the Fermi surface.


author="Stefan Kehrein, Andreas Mielke",
title="Theory of the Anderson impurity model: The Schrieffer-Wolff transformation re-examined",
journal="Ann. Physics (NY)",

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Last changes: 15.11.2017.