Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition
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.
Cite
@article{arxiv.1310.5800,
title = {Fermionic Functional Renormalization Group Approach to Superfluid Phase Transition},
author = {Yuya Tanizaki and Gergely Fejős and Tetsuo Hatsuda},
journal= {arXiv preprint arXiv:1310.5800},
year = {2014}
}
Comments
20 pages, 7 figures; title and abstract changed, fig.4 added, references added; typos corrected