Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition

Yuya Tanizaki, Tetsuo Hatsuda

Published Aug 14, 2016• 11 citations

Abstract

A fermionic functional renormalization group (FRG) is applied to describe the super-fluid 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 scat-tering 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 con-cerning their frequency/momentum dependence. We found that the fermion self-energy turns out to be substantial even in the weak couping region, and the frequency depen-dence 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. Subject Index A40, A63, B32, I22

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