Functional renormalization group approach to correlated fermion systems

By W. Metzner, Manfred Salmhofer, Carsten Honerkamp, V. Meden, K. Schoenhammer. 2011

465 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/a1ff2323d4fdb2f92fc6df1ea3ae563855cb1d5e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. A. Rubtsov
2. A. Eichhorn
3. Lukas M. Sieberer
4. M. Buchhold
5. L. Canet
6. W. Metzner
7. J. Moore
8. Shiwei Zhang

In Condensed Matter Physics

1. A. Rubtsov
2. Hartmut Hafermann
3. A. Eichhorn
4. Olivier Parcollet
5. M. Katsnelson
6. Michel Ferrero
7. L. Canet
8. M. Buchhold

Citations in the corpus

• Diagrammatic routes to nonlocal correlations beyond dynamical mean field theory (2017, methodology): “The functional renormalization group (fRG) approach [for a review see Metzner et al., 2012] provides an alternative way for generating nonlocal correlations beyond DMFT — through the fRG flow between the local problem and the corresponding lattice problem.”
• The nonperturbative functional renormalization group and its applications (2020, background): “Hertz-Millis theory can be formulated as a simple truncation of the bosonic FRG with few running couplings [484].”
• Tracking the Footprints of Spin Fluctuations: A MultiMethod, MultiMessenger Study of the Two-Dimensional Hubbard Model (2020, background): “• Other approaches: in this category we show results from the two-particle self-consistent approach (TPSC, TPSC+, [34–36]), the functional renormalization group (fRG [37], here considered up to one loop with Katanin substitution) and the parquet approximation (PA [38, 39]).”
• Keldysh field theory for driven open quantum systems (2015, background): “Indeed, it has proven a very versatile tool in many different physical context, ranging from quantum dots [234–236], ultracold atoms [233], strongly correlated electrons [237], classical stochastic models [238, 239], quantum chromodynamics [232, 240], to quantum gravity [241].”
• Physical realization of a quantum spin liquid based on a complex frustration mechanism (2016, background): “[39, 40]) then formulates an infinite hierarchy of coupled differential equations for the evolution of all m-particle”
• The physics of quantum materials (2017, background): “…by experimental observations on iron-based superconductors, the past years have seen rapid advances in theoretical methods—such as the functional renormalization group 46,47 —that treat moderately correlated-electron systems in an unbiased manner and with a minimum of uncontrolled approximations.”