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Weakly interacting electrons and the renormalization group
Author(s) -
Binz B.,
Baeriswyl D.,
Douçot B.
Publication year - 2003
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200310033
Subject(s) - physics , renormalization group , pairing , renormalization , fermi gas , quantum mechanics , fermi surface , functional renormalization group , electron , formalism (music) , fermi gamma ray space telescope , instability , superconductivity , theoretical physics , condensed matter physics , quantum electrodynamics , art , musical , visual arts
We present a general method to study weak‐coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high‐energy spin fluctuations create an effective attraction between the quasi‐particles. As an example, we show the occurrence of d ‐wave pairing in the repulsive Hubbard model in two dimensions. In one dimension or if the Fermi surface is nested, there are several competing instabilities. The required renormalization group formalism for this case is presented to lowest (one‐loop) order on a most elementary level, connecting the idea of the “parquet summation” to the more modern concept of Wilson's effective action. The validity and restrictions of the one‐loop approximation are discussed in detail. As a result, three different renormalization group approaches known in the literature are shown to be equivalent within the regime of applicability. We also briefly discuss the open problem of a two‐dimensional Fermi system at Van Hove filling without nesting.