Field-theoretical renormalization group for a flat two-dimensional Fermi surface

Abstract

We implement an explicit two-loop calculation of the coupling functions and the self-energy of interacting fermions with a two-dimensional flat Fermi surface in the framework of the field theoretical renormalization group (RG) approach. Throughout the calculation both the Fermi surface and the Fermi velocity are assumed to be fixed and unaffected by interactions. We show that in two dimensions, in a weak coupling regime, there is no significant change in the RG flow compared to the well-known one-loop results available in the literature. However, if we extrapolate the flow to a moderate coupling regime there are interesting new features associated with an anisotropic suppression of the quasiparticle weight Z along the Fermi surface, and the vanishing of the renormalized coupling functions for several choices of the external momenta.

16 pages and 22 figures

References in corpus (8)

• Nodal metallic behavior of lightly-doped La${}_{2-x}$Sr${}_x$CuO${}_4$
• Parquet solution for a flat Fermi surface
• Quasiparticle anisotropy and pseudogap formation from the weak-coupling renormalization group point of view
• Flow of the quasiparticle weight in the N-patch renormalization group scheme
• Exact renormalization group flow equations for non-relativistic fermions: scaling towards the Fermi surface
• Interacting Electrons on a Square Fermi Surface
• Correlation functions for a two-dimensional electron system with bosonic interactions and a square Fermi surface
• Fermi Surface Renormalization in Two Spatial Dimensions

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