4.4 Article

Weakly interacting electrons and the renormalization group

期刊

ANNALEN DER PHYSIK
卷 12, 期 11-12, 页码 704-736

出版社

WILEY-V C H VERLAG GMBH
DOI: 10.1002/andp.200310033

关键词

correlated electrons; Hubbard model; parquet summation; superconductivity

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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 modem 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.

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