Efimov effect from functional renormalization

Abstract

We apply a field-theoretic functional renormalization group technique to the few-body (vacuum) physics of non-relativistic atoms near a Feshbach resonance. Three systems are considered: one-component bosons with U(1) symmetry, two-component fermions with U(1)\times SU(2) symmetry and three-component fermions with U(1) \times SU(3) symmetry. We focus on the scale invariant unitarity limit for infinite scattering length. The exact solution for the two-body sector is consistent with the unitary fixed point behavior for all considered systems. Nevertheless, the numerical three-body solution in the s-wave sector develops a limit cycle scaling in case of U(1) bosons and SU(3) fermions. The Efimov parameter for the one-component bosons and the three-component fermions is found to be approximately s=1.006, consistent with the result of Efimov.Comment: 21 pages, 6 figures, minor changes, published versio

Functional renormalization group and conformal invariance in cold atoms

“…above the state with zero density n = 0 and zero temperature T = 0. As was shown in [9,10], numerous mathematical simplifications appear in the nonrelativistic vacuum compared with the many-body state. For instance, all Feynman diagrams with loop lines pointing in the same direction vanish.…”

“…It is remarkable that for the two considered systems the complicated flow equation (11) at E = 0 can be solved exactly [10], and the result coincides with the solution of the Skorniakov-Ter-Martirosian integral equation [15]. For illustration, we present a numerical solution of Eq.…”

“…Finally, in addition to the two systems discussed above, another interesting model of three-component fermions with S U(3)×U(1) internal symmetry was studied in [10]. It was demonstrated that this system exhibits the Efimov effect with the Efimov parameter s 0 identical to the bosonic case.…”

“…As advocated in [9,10], a systematic vertex expansion of Γ k is especially suitable for studies of few-body problems. The vertex expansion is an expansion in powers of fields, i.e.…”

“…3. The flow equation for P ϕ (Q) can be solved analytically [9,10], and the solution for bosons and fermions differs only by a simple multiplicative factor. Keeping in mind the question asked in the end of Sec.…”