Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition

Yuya Tanizaki; Gergely Fejős; Tetsuo Hatsuda

doi:10.1093/ptep/ptu035

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arXiv · 1310.5800

Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition

Yuya Tanizaki·Gergely Fejős·Tetsuo Hatsuda

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Abstract

Fermionic functional renormalization group (FRG) is applied to describe the superfluid phase transition of the two-component fermionic system with attractive contact interaction. Connection between the fermionic FRG approach and the conventional Bardeen-Cooper-Schrieffer (BCS) theory with Gorkov and Melik-Barkhudarov (GMB) correction are clarified in details 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 couping 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.

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Yuya Tanizaki, Gergely Fejős, Tetsuo Hatsuda. 2014-04-24. Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition. https://doi.org/10.1093/ptep%2Fptu035

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