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arXiv · 1003.4032

Universal and non-universal renormalizations in Fermi liquids

Andrey V. Chubukov·Dmitrii L. Maslov
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Abstract

We discuss an interplay between the Fermi-liquid (FL) theory and diagrammatic perturbative approach to interacting Fermi systems. In the FL theory for Galilean-invariant systems, mass renormalization $m^*/m$ comes exclusively from fermions at the Fermi surface. We show that in a diagrammatic perturbation theory the same result for $m^*/m$ comes from fermions both at and away from the Fermi surface. The equivalence of the FL and pertubative approaches is based on a particular relation between self-energy contributions from high- and low-energy fermions. We argue that care has to be exercised in the renormalization group approach to a FL in order not to miss the high-energy contribution to $m^*/m$. As particular examples, we discuss $m^*/m$ and the quasiparticle residue $Z$ for 2D and 3D systems with both SU(2) and SU(N) symmetries, and with a short-range interaction. We derive an expression for the anisotropic part of the Fermi-liquid vertex in the large-$N$ limit of the SU(N) case.

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Andrey V. Chubukov, Dmitrii L. Maslov. 2010-03-21. Universal and non-universal renormalizations in Fermi liquids. https://doi.org/10.1103/physrevb.81.245102

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