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A functional renormalization group approach to the Anderson impurity model.

Lorenz Bartosch¹, Hermann Freire, Jose Juan Ramos Cardenas

¹Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|August 11, 2011

Summary

We present a functional renormalization group method for the Anderson impurity model, improving descriptions of low-energy properties with intermediate interactions. This approach overcomes mean-field theory

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Area of Science:

Condensed Matter Physics
Quantum Many-Body Theory
Computational Physics

Background:

The Anderson impurity model is a fundamental model for understanding magnetism and electron correlations in materials.
Mean-field theory approximations often fail for strongly correlated systems, predicting unphysical instabilities.
Accurate description of low-energy properties, including the Kondo scale, remains a challenge for theoretical methods.

Purpose of the Study:

To develop a functional renormalization group (fRG) approach for the Anderson impurity model.
To describe low-energy single-particle properties accurately, particularly for intermediate on-site interactions.
To overcome limitations of previous theoretical methods, such as unphysical Stoner instabilities.

Main Methods:

Generalization of a previously proposed fRG method using two independent Hubbard-Stratonovich fields.
Inclusion of transverse and longitudinal spin fluctuations to capture correlation effects.
Development of a new truncation scheme for fRG flow equations using Dyson-Schwinger equations.

Main Results:

The developed fRG approach successfully removes the unphysical Stoner instability predicted by mean-field theory.
Spin fluctuations are incorporated, leading to a more realistic description of the system's behavior.
A specific decoupling scheme respecting spin-rotational invariance yields the lowest quasiparticle weight.

Conclusions:

The functional renormalization group method provides a robust framework for studying the Anderson impurity model.
The inclusion of spin fluctuations is crucial for accurately describing the low-energy physics.
The proposed truncation scheme offers a way to obtain closed flow equations for the fermionic self-energy.