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Functional renormalization group approach to correlated fermion systems

Walter Metzner, Manfred Salmhofer, Carsten Honerkamp, Volker Meden, and Kurt Schönhammer

Walter Metzner

  • Max-Planck-Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany

Manfred Salmhofer

  • Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg, Germany

Carsten Honerkamp

  • Institut für Theoretische Festkörperphysik and JARA-Fundamentals of Future Information Technology, RWTH Aachen University, D-52056 Aachen, Germany

Volker Meden

  • Institut für Theorie der Statistischen Physik and JARA-Fundamentals of Future Information Technology, RWTH Aachen University, D-52056 Aachen, Germany

Kurt Schönhammer

  • Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, D-37077 Göttingen, Germany

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Rev. Mod. Phys. 84, 299 – Published 12 March, 2012

DOI: https://doi.org/10.1103/RevModPhys.84.299

Abstract

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems; (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals; and (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and nonequilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. A self-contained derivation of the exact flow equations is presented and frequently used truncation schemes are described. Reviewing selected applications it is shown how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.

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Rev. Mod. Phys. 84, 299– Published 12 March, 2012
  • Received 4 April 2011

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