Multi-regulator functional renormalization group for many-fermion systems

Tobias Müller, Yasir Iqbal, Johannes Reuther +1 more

Carsten Honerkamp A

Yuya Tanizaki, Tetsuo Hatsuda

We propose a method of multi-regulator functional renormalization group (MR-FRG) which is a novel formulation of functional renormalization group with multiple infrared (IR) regulators. It is applied to a two-component fermionic system with an attractive contact interaction to study crossover phenomena between the Bardeen–Cooper–Schrieffer (BCS) phase and the Bose–Einstein condensation (BEC) phase. To control both the fermionic one-particle excitations and the bosonic collective excitations, IR regulators are introduced, one for the fermionic two-point function and another for the four-fermion vertex. It is shown that the Nozières–Schmitt-Rink (NSR) theory, which is successful to capture qualitative features of the BCS–BEC crossover, can be derived from MR–FRG. Some aspects of MR-FRG to go beyond the NSR theory are also discussed.

Walter Metzner

Yuya Tanizaki

New formulation of fermionic functional renormalization group (f-FRG) with multiple regulators is proposed. It is applied to a two-component fermionic system with an attractive contact interaction in order to study the whole region of the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover. Combining a conventional formalism of FRG with a two-point infrared (IR) regulator and a new formalism with an IR regulator inside the four-fermion vertex, we control both one-particle fermion excitations and collective bosonic excitations. This justifies a simple approximation on the f-FRG method, so that the connection of the f-FRG formalism to the Nozi\`eres-Schmitt-Rink (NSR) theory is made clear. Aspects of f-FRG to go beyond the NSR theory are also discussed.

Yuya Tanizaki

Fermionic functional renormalization group is applied to describe Bose-Einstein condensation of composite dimers in a two-component fermionic system with a short-range interaction. Since fermions are bounded in dimers, they do not affect long-range nature of the system. This requires us to invent a renormalization group procedure, which controls the dispersion relation of composite bosons without affecting that of fermionic excitations. In order to realize it without introducing auxiliary bosonic fields, we introduce a vertex infrared regulator so as to compute the critical temperature.