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

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

1999-12-20

arxiv.org/abs/cond-mat/9912368v1

Physics

Condensed Matter

Superconductivity

4 pages, no figures

Scientific paper

10.1103/PhysRevLett.85.361

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.

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