A Rigorous Proof of Fermi Liquid Behavior for Jellium Two-Dimensional Interacting Fermions

Abstract

Using the method of continuous constructive renormalization group around the Fermi surface, it is proved that a jellium two-dimensional interacting system of Fermions at low temperature $T$ remains analytic in the coupling constant $\lambda$ for $|\lambda ||\log T|\le K$ where $K$ is some numerical constant and $T$ is the temperature. Furthermore in that range of parameters, the first and second derivatives of the self-energy remain bounded, a behavior which is that of Fermi liquids and in particular excludes Luttinger liquid behavior. Our results prove also that in dimension two any transition temperature must be non-perturbative in the coupling constant, a result expected on physical grounds. The proof exploits the specific momentum conservation rules in two dimensions.

4 pages, no figures

References in corpus (1)

• Renormalization group analysis of the 2D Hubbard model

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