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.

20 pages, 7 figures; title and abstract changed, fig.4 added, references added; typos corrected

References in corpus (11)

• Exact evolution equation for the effective potential
• Observation of Bose-Einstein Condensation of Molecules
• Thermodynamics of the BCS-BEC crossover
• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Critical Temperature Curve in the BEC-BCS Crossover
• Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity
• Particle-hole fluctuations in the BCS-BEC Crossover
• Pairing and Superfluid Properties of Dilute Fermion Gases at Unitarity
• Unitary Fermi gas at finite temperature in the epsilon expansion
• Renormalization group approach to interacting fermion systems in the two-particle-irreducible formalism
• Effective interactions and fluctuation effects in spin-singlet superfluids

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