arXiv:1310.5800 · Progress of Theoretical and Experimental Physics

Fermionic functional renormalization group approach to superfluid phase transition

Yuya Tanizaki, G. Fej s, T. Hatsuda

Published Apr 1, 2014• 14 citations

Abstract

A fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. The connection between the fermionic FRG approach and the conventional Bardeen–Cooper–Schrieffer (BCS) theory with Gorkov and Melik-Barkhudarov (GMB) correction are clarified in detail in the weak coupling region by using the renormalization group flow of the fermionic four-point vertex with particle–particle and particle–hole scattering contributions. To go beyond the BCS+GMB theory, coupled FRG flow equations of the fermion self-energy and the four-point vertex are studied under an Ansatz concerning their frequency/momentum dependence. We found that the fermion self-energy turns out to be substantial even in the weak coupling region, and the frequency dependence of the four-point vertex is essential to obtain the correct asymptotic-ultraviolet behavior of the flow for the self-energy. The superfluid transition temperature and the associated chemical potential are calculated in the region of negative scattering lengths.

DOI: 10.1093/ptep/ptu035

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